What Do X Mean in Math

Introduction to math variable x means:

In mathematics a variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use. The concepts of constants and variables are fundamental to all modern mathematics, science, and engineering .Here we are going to study about what is math variable x means and how to solve the value of x with example problems.    (Source from Wikipedia).

Example problems :


Math example: 1

Find the value of |x+3| = 0

Solution:

Here x means the modulus value

We have take -(x+3) and x +3

-x -3 = 0

Add the +3 both sides

-x = 3

x = -3

Similarly   x + 3 = 0

Add both sides -3

x + 3-3 = -3

x = -3

Therefore the solution x = -3, -3

Math example 2:

Solve for x in the equation 4x + 6 + 6x = 46

Solution:

Here x means unknown value we have to find the x value.

First we have to combine the like terms here the like terms are x.

4x + 6x = 10x

10x + 6 = 46

Add both sides -6 we get

10x + 6 - 6 = 46 -6

10x = 40

Divide both sides 10 we get

x = 40/10

x = 4

Therefore the value of x = 4



Some more examples of x mean in math:


Math problem 3:

4x+3+2x + 5 > 2x+4

Solution:

Here x means inequality variable we have to find the x value

In the left hand side combine the like term first

4x+3+2x +5 > 2x+4

6x + 8 > 2x + 4

Add both sides -4 we get

6x + 8 - 4 > 2x + 4 - 4

In right hand side 4 - 4 will be cancelling

6x+ 4 > 2x

Add both sides -2x

6x -2x + 4 > 2x -2x

4x + 4 > 0

Add both sides -4 we get

4x + 4 -4 > -4

4x > -4

Divide both sides 4 we get

(4x / 4) > - `(4/4)`

x > - `(4/4)`

x > -1

Therefore the x value greater than -1

Second Derivative

The derivative of the derivative of a given function is the second derivative. Given a function f(x), the 2nd derivative is represented as f’’(x) of [f(x)]. The definition of second derivative of a function f(x) at a point a is, f’’(x) = lim(x?a [f’(x) – f(a)]/(x-a)

It gives how fast the rate of change of a function is changing. It gives the information about the concavity.
Second Derivative Curvature
The curvature of a given function is described by the second-derivative of the function.  If the function curves upwards then the curvature of the function is concave up and if the function curves downwards then the curvature of the function is concave down.

The function behavior corresponding to its 2nd derivative can be given as follows:
If f’’(x)>0, then the curvature of the function f(x) is concave up
If f’’(x)<0 br="" concave="" curvature="" down="" f="" function="" is="" of="" the="" then="" x="">If f’’(x)=0, then it corresponds to a possibility of an inflection point
The inflection point is the point where there is a change in the concavity of the function f(x).

Calculate Second Derivative

While calculating the 2nd derivative the 1st derivative becomes the function.

The two basic steps involved in finding the second of the derivative are as follows:
Step1:  first the derivative of the function is found. The result thus obtained becomes the function to find it
Step2: the derivative of the first derivative gives the required derivative
If y=4x3- 3x^2 + 5x
Step1: The first derivative is given by y’ = [4x3 – 3x^2 + 5x]. Taking derivative of each of the terms,
y’= [4x3] – [3x^2] + [5x]
= 12x^2 – 6x + 5
Step2: Now the function is y’= 12x^2 – 6x + 5. The second-derivative would be,
y’’ = [y’]
= [12x^2 – 6x + 5] taking derivative of each of the terms,
= [12x^2] – [6x] + [5]
= 24x – 6 + 0
So, y’’ = 24x- 6 required 2nd derivative of y



Acceleration Second Derivative

Instantaneous velocity of a particle along a line at time t is the first derivative of a function which represents its position along a line at a particular time t. The derivative of this velocity is the second-derivative of the function which is the instantaneous acceleration of the particle at a time t.
For instance, let y= p(t) is the position of the particle, then  the instantaneous velocity which is the first derivative is v=p’(t)and the instantaneous acceleration of the particle at time t which is the second derivative is a=v’(t) = p’’(t).

Variable in Math

Introduction to variable in math:

In mathematics, the term “variable” is used in algebra. Variable is nothing but the letter which represents the some numerical value. For example consider the algebraic expression 4x. Here 4 is the constant and x is the variable.

Discuss:

(a)   Consider x + y = 10.

The variable x and y are variables and they has some numerical values that makes the above statement true.

Examples:

1. P = 4s    2. x + 5 = 10

Here

4, 5, 10 are constants.

P, s, x are variables.

Note:

The numbers are constants.

To denote variable in math we use the alphabets A to Z or a to z.

Let us see some example problems.


Variable in math - Example problems:


1. Pick out the constants in the following:

8, a, x, y, – 25, 0, z, 35, 2.7,

Solution:

The constants are 8, – 25, 0, 35, 2.7 and

2. Pick out the variables in the following:

63, x, 27, m, p, q, 10, 0, y

Solution:

The variables are x, m, p, q and y

2. Pick out the variables and constants: A, – 15, q, l, 22.3, 73

Solution:

The variables are A, q and l

The constants are – 15, 22.3 and 73.

Practice problems:

1) Pick out the variables in the following:

6, c, – 12, h, k, 16, m, n, – 22, p, s, 30

2) Write any five variables:



Power of the variable in math:


In math, the product of 18 and a is 18 × a and it is written as 18a .Similarly the product of two literals a and b is a × b = ab

Now let us see how the repeated product of a literal with itself is written in math.

Multiply a with a. We get a × a and is denoted by a2.

We read a2 as a to the power of 2. Similarly d × d × d = d3, which is read as m to the

Power of 3

In a2, 2 is the power and a is the base.

In d3, 3 is the power and d is the base.

Example problems using the variables:

a + 5 = 10. Find the value of a.

Solution:

To find the value of a, we have to move the like terms in one side

For that, subtract 5 on both sides

a + 5 – 5 = 10 – 5

Simplify,

a + 0 = 5

a = 5.

Answer to 4th Grade Math

Introduction about answer to 4th grade math:

In mathematics, the following topics are covered under 4 th grade, these 4th grade mostly deals with the number system, algebra terms, basic geometry shapes and their way of solving techniques , order of operations. Now, here we are going to discuss about the different type of problems and their answers.



Description to answer to 4th grade math:


The following areas are covered under the 4th grade  math:

Natural Numbers

The natural numbers are normal numbers which starts with 1,2,3…we can call these numbers as a counting numbers.

Even and odd numbers

When a number is divisible by 2 then its called as even number and the remaining numbers are all odd numbers.

Even numbers are 2,4,6… and odd numbers are 1,3,5…

Fractions

Fraction is looking line division operation in which the denominator is always less than the numerator and this is a proper fraction. For example: 6/3.The opposite of proper fraction is called improper fraction. For example 5/7. Here we have another type of fraction is said to be mixed fraction. A mixed fraction is a combination of whole number and proper fraction, for example 5 8/4

Algebraic equation

It can be any equation with the arithmetic operation operators.

Algebraic expression

Here we have the different term with the different sign and operations.

Geometry shapes:

In 4th grade we have lot of geometry shapes like square, rectangle, circle, etc….



Problems with answers to 4th grade math:


Some of 4th grade math problems with answers:

Example 1:

Solve: 5( 4+1) – 9 + 3( 7 ) + 26

Answer:

5( 4+1 ) – 9 + 3( 7 ) + 26

=  5( 5 ) – 9 + 21 + 26

=  25 - 9 + 47

=  63



Example 2:

Simplify : 4/12 +5/15

Answer:

4/12+6/12 = 4+6/12

=10/12

=5/6


Example 3:

Simplify:      5( x + 6 )  =  65

Answer:

5( x + 6 )  =  65

5x + ( 5 x 6 )  =  65

5x + 30  =  65

5x   =  35

x   =  7


Example 4:

Martin bought a bike  for 40 and he sold it for 47. calculate the gain?

Answer:

Original cost price of bike =  $ 40

sold price of bike =  $ 47

Gain  =  sold price - Cost Price

=  47 - 40

=  $ 7

So he the gain as $7.

4th Grade Math Probability

Introduction to 4th grade math probability:

Generally probability is defined as the ratio of the number do ways of an event occur to the total number of possible outcomes, probability is used in the area of statistics, finance, gambling and science.

Probability formula for 4th grade math probability

The probability of event P (A) = no of possible events n (a) `//` the total number of the events n(s)

Example problem -4th grade math probability


Suppose a single die is rolled find the probability of getting odd number and also even number? ii) Probability of getting each number?

Solution:

Generally the die has 6 sides ,they are numbered as 1,2,3,4,5,6

From the six  number  we can tell the odd number as  1,3,5 and even number as 2,4,6

Here the possible outcomes of these experiments are 1, 2, and 3,4,5,6.

First we have to find the probability of getting odd number, the die as 3 odd numbers

So the probability p (odd) =3/6

Here 6 is the total number

Similarly the probability of even number will be written as

Probability p (even) =3/6

ii) Probability of getting each number it will be shown as below,

P (1) =1/6

P (2) =1/6

P (3) =1/6

P (4) =1/6

P (5) =1/6

P (6) =1/6

Example problem -4th grade math probability

Here the circle is divided into 8 equal parts and they are colored using the different color find the probability of choosing green color?

Solution:

It is divided into equal parts so the total number will be present in the denominator and counts the how many colors are shaded using green, here colors are shade in a green so it must be come in the numerator parts

Then the answer is 4/8



Example problem -4th grade math probability


A basket contains the fruits, it has 5 apples, 3 orange, 11 mango and 1plum what is the probability of choosing mango without looking the basket?

Solution:

The total number of fruits is 5 apples, 3 orange, 11 mango and 1plum so the total number of fruits in the basket is 5+3+11+1=20

P (mango) =11/20

Here numerator represents the count of apple and denominator represents the total count of fruits

Doing Math Problem

Introduction for Mathematics:

Mathematics is one of the most important terms in our daily life. We have seen so many different concepts in mathematics.  In mathematics, many formulas are present.  The formulas are used to solve all types of problems.  Here, we are going to see some mathematical problems in some different concepts.



Example problems – Doing math problem


Example for doing math problem 1:

Writing the simple mathematical form: 36/6.

Solution:

Given 36/6

First, we are going to factor the numerator value and then factor the value of denominator.

At last, decrease the fraction value by removing the common value.

In the given problem, 36 is the numerator and 6 is denominator

Here, 6 is the common for numerator and denominator.

36 / 6 = 6

Now, we get the answer 6.

Answer: 6

Example for doing math problem 2:

Subtract 34mn + 20n – 28m from 40mn - 22n + 24m.

Solution:

The given equations are 34mn + 20n – 28m and 40mn - 22n + 24m

Subtract these two equations

34mn + 20n – 28m – (40mn - 22n + 24m)

Process 1: Add the subtract value within the parenthesis

Now, we get 34mn + 20n – 28m – 40mn + 22n - 24m

Process 2:

Arranging the values in term

= 34mn – 40mn + 20n + 22n – 28m – 24m

= -6mn + 42n – 52m

The correct answer is -6mn + 42n – 52m.



Example for doing math problem 3:

Solve (10p + 17q) + (12p – 14q)

Solution:

Process 1:

First, we are going to solve within the parenthesis,

10p + 17q + 12p – 14q

Process 2:

Now, we are going to arrange in terms,

= 10p + 17q + 12p – 14q

= 10p + 12p + 17q – 14q

Process 3:

Here, we are going to add,

= 10p + 12p + 17q – 14q

= 22p + 3q

The correct answer is 22p + 3q.

Example for doing math problem 4:

Find a in the 24a + 3b + 3a = 0, the value of b is a - 10.

Solution:

The given equation is 24a + 3b + 3a = 0

Substitute the value b in this given equation

24a + 3(a - 10) + 3a = 0

24a + 3a – 30 + 3a = 0

Arranged in terms

24a + 3a + 3a – 30 = 0

30a – 30 = 0

30a = 30

a = 30/30

a = 1

Answer:  The value of a is 1.


Practiced problem – Doing math problem


Doing math practiced problem 1:

Solve (2p + 3q) - (4p – 5q)

Answer: -2p +8q

Doing math practiced problem 2:

Find x in the 15x + 5y – 5x = 0, the value of y is x - 1.

Answer:  1/3

Properties Of Math

Introduction to math properties:

Mathematics is the important study which is applied in all fields. There are many properties in math. These properties define some of the rules and methods for solving the problems. Some of the properties in math are,

Associative property
Distributive property
Commutative property
Reflexive property
Transitive property
Addition property
Multiplication property
Additive identity
Symmetric property
Multiplication identity
Substitution property.



Math properties


Properties in math:

Here we are going to discuss about some of the properties in math.

Associative property:

In the associative property we does not consider the way that how the numbers are grouped with others. In this property when we rearrange the parenthesis it does not changes the value. This property is common for both addition and multiplication. The associative property is given as,

( p + q ) + r = p + ( q + r)

( p * q ) * r = p * ( q * r)

Commutative property:

In this commutative property we can swap the numbers after performing the operation. Since the value does not change even after the swapping or interchanging. This property is also common for both addition and multiplication. This commutative property is given as,

p + q = q + p

p * q = q * p

Distributive property:

In this distributive property, we can split and broken up the number of parts. The distributive property is given as,

p * (q +r) = p * q +p * r

Additive identity:

When we add zero to a number it results the same number as the answer. This property is referred as additive identity.

p + 0 = p.

Multiplicative identity:

When we multiply one to a number then it will result the same number as the answer which is referred as property of multiplicative identity. This property is given as,

( p ) 1 = p.

Addition property:

When two numbers such as p = q is given then if we add r to both numbers p and q then this property is referred as addition property. The addition property is given as,

p = q, p + r = q + r.

Multiplication property:

This property is same as the addition property but in this instead of addition we want to do multiplication. This multiplication property is given as,

p = q, pr = qr.


Example problems


Example problems by using the properties of math:

Problem 1: Simplify the given equation 4x – 5y + 8x.

Solution:

Given: 4x – 5y + 8x.

Step 1: By using the commutative property write the given equation as,

4x + 8x – 5y

Step 2: According to the associative property, write the equation as,

(4x + 8x) – 5y

Step 3: By using distributive property write the equation as,

x ( 4 + 8) – 5y

Step 4: Finally according to the commutative property and by doing the simplification, the equation is given as

12x – 5y

Problem 2: simplify: 7 ( x + 4).

Solution:

Given: 7(x + 4)

Step 1: By using the distributive property write the given equation as,

7x + 7 * 4 – 6x

Step 2: After doing simplification according to the commutative property, write the equation as,

7x – 6x +28

Step 3: By using associative property write the equation as,

( 7x – 6x ) + 28

Step 4: According to the distributive property, the equation is given as

x( 7 – 6) + 28

Step 5: According to the commutative property, the equation is given as,

x + 28.