Equations with variables on both sides

Grade 8 Math Worksheets

We can see some equations where variable (the unknown quantity) appears on both sides of an equation. We can solve such equations in the same way as we solve equations with numerical values on both sides.

Let us see the example below:

8x = 5x + 9

Subtracting 5x from both sides,

8x – 5x = 5x + 9 – 5x

3x = 9

Divide by ‘3’ on both sides, we get x = 3

Example: Solve for x, if 5x + 4 = 18 + 3x

Subtract 3x and 4 from both sides, 5x + 4 = 18 + 3x

5x + 4 – 3x – 4 = 18 + 3x – 3x – 4

2x = 14

Divide by ‘2’ on both sides, we get x = 7

Check your answer: Put x = 7 in 5x + 4 = 18 + 3x

L.H.S = (5 × 7) + 4 = 35 + 4 = 39

R.H.S = 18 + (3 × 7) = 18 + 21 = 39

Since L.H.S = R.H.S, so x = 7 is the answer.

Check Point

Solve for x: 2x + 9 = 5x
Solve for y: 3y + 1 = 4y + 12
Solve for x: 3x + 3 = 4x – 8
Solve for y: 2y – 10 = 7y
Solve for z: 20 – z = 16 – 5z

Answer key

3
-11
11
-2
-1

Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE Demo Session.

Schedule a Free Session

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

Pricing for Personalized Online Tutoring

Tutoring Package	Validity	Grade (1-12), College
5 sessions	1 Month	$119
1 session	1 Month	$24
10 sessions	3 months	$229
15 sessions	3 months	$339
20 sessions	4 months	$429
50 sessions	6 months	$999
100 sessions	12 months	$1949