# VARIABLES ON BOTH SIDES

## About "Variables on both sides"

How to solve equations with variables on both sides :

Solve means finding the value of the variable given  in the question. When we solve equations with variables on both sides, first we have to identify the variable for which we need to find the value.

• Now we have to bring the variables one side of the equation, usually we prefer left side. In order to move variables from right side to left side we have to use inverse operations.
• Bring the numerical values to the other side. Usually we prefer right side. In order to move the values to the right side, we have to use inverse operations.

Let us see some example problems to understand of solving these kind of problems.

Example 1 :

Solve 2x + 3 = 5x - 2

Solution :

Step 1 :

In order to bring + 5x to the left side, we have to subtract 5x on both sides.

2x + 3 = 5x - 2

2x - 5x + 3 = 5x - 5x - 2

-3x + 3 = -2

Step 2 :

In order to bring +3 to the right side. So, we have to subtract 3 on both sides.

-3x + 3 - 3  = -2 -3

-3x = -5

Step 3 :

Since -3 is multiplied by x, to isolate x we have to divide by -3 on both sides.

-3x/(-3) = -5/(-3)

x = 5/3

Example 2 :

Solve  −7x − 3x + 2 = −8x − 8

Solution :

Step 1 :

−7x − 3x + 2 = −8x − 8

Combining -7x and -3x we will get -10.

-10x + 2 = -8x - 8

Now we have to bring -8x to the left side, so we have to add 8x on both sides.

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

subtract 2 on both sides

-2x + 2 - 2 = - 8 - 2

-2x = -10

divide by -2 on both sides

-2x/(-2) = -10/(-2)

x = -5

Example 3 :

Solve  −6n − 20 = −2n + 4(1 − 3n)

Solution :

Step 1 :

Distribute 4 with 1 and -3n

−6n − 20 = −2n + 4(1 − 3n)

−6 n − 20 = −12 n + 4

Add 12 n on both sides

-6n + 12n - 20 = -12n + 12n + 4

6n - 20 = 4

6n - 20 + 20 = 4 + 20

6n = 24

Divide by 6 on both sides

6n/6 = 24/6

n = 4

Example 4 :

Solve -8n + 4(1 + 5n) = −6n − 14

Solution :

Step 1 :

-8n + 4(1 + 5n) = −6n − 14

Distribute 4

-8n + 4 + 20n = −6n − 14

12n + 4 = -6n - 14

12n + 6n + 4 = -6n + 6n - 14

18n + 4 = -14

Subtract 4 on both sides

18n + 4 - 4 = -14 - 4

18n = -18

divide 18 on both sides

n = -18/18

n = -1

Example 5 :

Solve 7(5a − 4) − 1 = 14 − 8a

Solution :

Step 1 :

7(5a − 4) − 1 = 14 − 8a

Distribute 7

35a - 28 - 1 = 14 - 8a

35a - 29 = 14 - 8a

35a + 8a - 29 = 14 - 8a + 8a

43a - 29 = 14

43a - 29 + 29  = 14 + 29

43a = 43

divide 43 on both sides

a = 1

After having gone through the stuff given above, we hope that the students would have understood "Variables on both sides".

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