How to Solve X: Learn Various Solving Methods

Algebra is a subject that most struggle with whether they have just started learning the algebraic expressions or are on their way to mastering the craft. Among all the issues, most students fail to understand how to solve x. To simply put, x is the missing value of a variable in an algebraic expression. Therefore, if you know the method of solving an expression, you can easily find the value of x. Unfortunately, the statement is easier said than implied. If you are having issues solving the value of x in an algebraic equation, this blog can take your breath away. Here, we have explained the basic algebraic expressions and shared the 5 easiest methods to solve the value of x.

What Do Equations Of X Signify In Math?

An equation means that both sides of the conjunction ‘=’ are equal.   It indicates that the value of the left-hand side of = must be the same as the value of the right-hand side. Take a look at the equation 10 – x = 5.

Here, the value of x is 5. It is because 10 – 5 = 5.

Thus, the value of both sides of the symbol ‘=’ is the same.

Note, in an algebraic equation, x is a variable whose value changes according to the equation. When you find the value for the variable x, it is called a solution. Just like in this case, the solution is 5.

Also read: Math Research Topics That Will Boost Your Academic Scores

Get to Know How to Solve X

Every student who studies math in school comes across algebra. It is a branch of math in which letters and other typical symbols are applied to signify numbers and values in formulas and equations. X is one of the variables used in algebra just like Y, Z, A, and other such variables. Now, if you want to know how to find the value of x, then you must be aware of the fundamental algebraic operations.

Isolate the x

One of the easiest methods of solving X is separating X on one side and moving the other numbers to the other side. If the number is a positive integer, it will turn into a negative when it moves to the other side and vice versa.

For example, the following is your equation

X + 9 = 16.

So, in this case, if you move the positive integer, +9 from the left side of the = to its right side, it will become a negative integer, -9. Then it will turn out to be as follows –

X = 16- 9.

Now, the variable X lies on one side of the equation. So it has become easy for you to find out how to solve X. You just have to solve the right-hand side of the equation. Once you subtract 9 from 16, you get the value of X.

So the answer turns out to be as –

X = 16 – 9 = 5.

This is the value of X is 5.

Keep negative numbers on one side

The second method to find how to solve x is by separating the negative numbers from the positive numbers. You keep the negative integers on one side of the = and positive integers on the other side.

For example, you are given an equation X – 5 =4.

To solve this equation and find the value of x you must send 5 to the right-hand side of the equation. Hence, it is evident that by moving the negative numbers to the other side, it becomes positive and easily determines the value of x. hence, the equation now turns out to be x = 4 + 5. Finally, the result turns out to be x = 9.

Solving multiplication

Suppose you are asked to find the multiplicative value of X in the equation X x 5 = 25.

To learn how to solve X, keep the numerals on one side of the equation and X on the other side. The easiest way is to send 5 to the other side of the equitation. However, don’t add or subtract the numerals like it is done in the examples discussed above. It is a problem with multiplication. Therefore, divide 5 by 25. Hence, the equation will be:

X = 25/5

As a result, the value of X is 5

Solving division

Finding how to solve x in a division equation is similar to the method you use to find a solution through multiplicative methods.

For example, you want to find the value of X in the equation X / 5 = 5.

In that case, you must first alter the position of 5 from the left-hand side of the equation to the right-hand side. However, in case of changing the position of a denominator from one side of the equation to the other, it appears as a numerator on the other side of the equation. Moreover, it is multiplied by the existing number. Consequently, this equation turns as,

X= 5×5

Then, the final value of X is 25.

Finding the value of X in the presence of multiple numbers

When you have an equation that consists of multiple numbers and you have to find the value of x, the method seems confusing. However, the rules are as simple as the ones used in the examples above. For instance, you have the following equation:

X -1 + 6 = 10.

Now, to find the value of X, simply move all the numerals to the right-hand side of the equation keeping X on the left-hand side of the equation. Make the positive integers negative and negative integers positive. Therefore, ‘-1’ will become ‘+1.’ Similarly, ‘+6’ will become ‘-6.’ The equation will turn out as:

X = 10 +1 -6

Hence, the value of X is 5.

These are the basic rules that you must follow to follow while you find the value of X. However, when you solve the algebraic expressions, the equation will not be as simple as the ones stated above. Then, how to solve X for those expressions? Choose the methods discussed below.

Also read: Importance of Math in Our Daily Life

Simple Methods To Solve The Value Of X

These are the simplest methods of solving the value of X. You will find it handy whether you have just begun solving algebraic equations or you are slowly turning out to be a master in this branch of math. Keep them in mind and implement them as and when required.

1. Basic Linear Equations

You call an algebraic equation a basic linear equation when each term present in the equation has one exponent and the equation can be presented in one straight line. Take a look at the example below and understand how the value of X is solved.

Find the value of x in the equation: 2² (x+3) + 9 – 5 = 32.

Solution:

2² (x+3) + 9 – 5 = 32

4(x+3) + 9 – 5 = 32

4x + 12 +9 – 5 = 32

It can be written as

4x + 16 = 32

4x = 16

It will become

4x + 16 -16 = 32

4x = 16

x = 4.

Now, if you want to check whether the derived value of x is accurate, place 4 in place of x in the equation. Then, see whether the value on the left-hand side of the equation equals the right-hand side.

2² (4+3) + 9 – 5 = 32

4(4+3) + 9 – 5 = 32

16 + 12 + 4 = 32

32 = 32

2.  Using Exponent

Exponent is a symbol used in the raise to a power method. It denotes the common mathematical term ‘to the power of’, ‘square root of’ or ‘cube root of’, etc.  In this method, the exponent increases the power of the number at the base to the power used as an exponent. This method helps in solving the value of x. Take a look at the example below to understand the solution.

Find the value of x in the expression 2x² + 12 = 44.

Solution:

2x² + 12 = 44

Next, 2x² + 12 – 12 = 44 -12

2x² = 32

2x²/ 2 = 32/2

x² = 16

Now, when you use the square root of the x², it will cancel the value of the exponent ^2. So upon squaring both, the left-hand side and the right-hand side, you will be left with x on the left-hand side of the equation and positive and negative square rooted values of 16 on the right-hand side.

Therefore x = √16

Hence, x = ± 4

Now to check whether you have inserted the accurate answer, put either + 4 or -4 in place of x and see the result. If both sides of the equation match with each other, your answer is accurate. Let us check whether the derived answer is accurate or not.

2x² + 12 = 44

2(4)^2 +12 = 44

2 X 16 + 12 = 44

32 + 12 = 44

Then, 44=44

3.  Using Fraction

A fraction is a section of a whole number. In algebra, it is expressed as a quotient, where the numerator is divided by the denominator. In simple fractions, both the numbers denote individual integers whereas a complex fraction has a fraction in the numerator or the denominator. Moreover, if the fraction appears as a proper fraction, the value of the numerator will always be less than the value of the denominator. Let us learn to find the value of x using a fraction from the example below:

Find the value of x from the equation

Solution:

The best way to find the solution to the expression  is to cross-multiply the numerals

Then, the equation becomes 3(x+3) = 2(6)

3x + 9 – 9 = 12 – 9

3x = 3

Then, x = 1

Now, to check the answer put the value of x = 1 in the equation and observe the result:

(cross multiplying the digits)

3 (1+3) = 2(6)

It will become

3+9 = 12

12=12

4.  Applying Radical Sign

The radical sign is a form of the square root of a number. It typically denotes a number that when multiplied by itself gives the original number. Here is an example of using a radical sign to find the value of x.

Example, find the value of x in the equation √ (2x + 9) – 5 = 0

Solution

√ (2x + 9) – 5 +5 = 0 + 5

√(2x + 9) =  5

Now, upon squaring both sides of the equation x comes under the radical sign.

Then, the equation becomes √ (2x + 9)² = 5²

Or, 2x+9 = 25

Write it as,

2x + 9 – 9 = 25 – 9

2x = 16

x = 16/2

x = 8

Now, take the following steps to check your work.

√( 2x+9) – 5 = 0

It can be written as

√( 2(8) + 9) – 5 + 5 = 0 + 5

√ (2(8)+9) = 5

Now, upon squaring both sides you can remove the square root.

2(8)+9 ^2 = 5^2

16 + 9 – 9 = 25 – 9

16 = 16

Also read: How to Solve Math Assignment Problems Faster?

5. Using Absolute Value

The absolute value of a real number x is the nonnegative value of x irrespective of the sign. It is denoted by the symbol “|”, located on both sides of the expression. Therefore, you write the absolute value as |−8|  and the value of the number is 8. Here is an example of finding the value of x using the Absolute value.

Example, find the value of x in the expression |4x+2| – 6 = 8

Solution:

|4x+2| – 6 = 8

Next, it will become

|4x+2| – 6 + 6 = 8

|4x+2| = 14

Now, to remove the absolute value and solve the equation, subtract 2 from both sides of the equation.

4x + 2 – 2 = 14 – 2

Next, it will become

4x = 12

x = 12/4

x = 3

Now, take away the absolute value and change the sign of the integers on the opposite side of x.

Then, the equation becomes 4x + 2 – 2 = – 14 – 2.

Hence, 4x = -16

x = -16/4

x = -4

Now, to check if you have found the exact answer first put the value of x = 3 in the equation |4X + 2| – 6 = 8 and see the results.

|4X + 2| – 6 = 8

|4(3) + 2| – 6 + 6 = 8 + 6

|4(3) + 2| = 14

Then, take away the absolute value and resolve the equation,

4 X 3 + 2 – 2 = 14 – 2

4 X 3 = 12

12 = 12

Conclusion

We often feel confused about how to solve x in mathematics and algebraic equations. However, if we know the technique, reasoning, and logic behind it, the solution becomes quite easy. Reading the blog post above will give you the pathway to solving the equation where you have to solve the value of x. However, if you still struggle with the task, take guidance from our experts. The research scholars of our team have been offering mathematical guidance and helping students solve algebraic equations easily for a long time.