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Level 5-6 Algebra - Equations with Letters on Both Sides

Solve equations with letters on both sides. Move terms, keep balance, and find unknowns using inverse operations and neat steps.

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Fascinating Fact:

In computer science, algorithms use similar balancing logic to compare changing values during calculations.

In KS3 Maths, you solve linear equations where letters appear on both sides of the equals sign. Bring like terms to one side, numbers to the other, keep operations balanced, then divide to find the unknown and check by substitution.

Key Terms

Variable: A letter that stands for an unknown number, such as x or y.
Like terms: Terms with the same variable and power that can be combined, e.g., 2x + 5x = 7x.
Balance method: Doing the same operation to both sides of an equation to keep it equal.

Frequently Asked Questions (Click to see answers)

How do I solve an equation with letters on both sides?

Collect letters on one side and numbers on the other. Example: 3x + 7 = 2x + 12 → subtract 2x: x + 7 = 12 → subtract 7: x = 5.

What mistakes should I avoid when moving terms?

Don’t change signs incorrectly. When you subtract 2x from both sides, subtract it from the whole side. Always perform the same operation on both sides.

What if there are negatives or fractions in the equation?

Work step by step. For negatives, keep track of signs. For fractions, multiply both sides by a common denominator to clear fractions before solving.

Try These Related Quizzes

1 .

Look at this equation: 10x + 18x = 7x + 189. Now decide which of the following is not correct.

10x + 18x + 7x = 189

10x + 18x - 7x = 189

21x = 189

x = 9

When we rewrite the equation as 10x + 18x - 7x = 189, we've moved the 7x from one side of the equals sign to the other. That means that it changes from a positive to a negative number

2 .

What is the value of e in the following equation: 2(e + 5) = 44?

0.7

2(e + 5) = 44 is the same as 2e + 10 = 44 so 2e = 34. 34 divided by 2 = 17

3 .

Look at the equation 4(a - 4) = 3a - 9. Now decide which of the following is not correct.

4a - 16 = 3a - 9

a = -9 + 16

a = 7

a = 25

Simplifying equations makes them a lot easier to solve

4 .

x + 7 = 10 + 12 is the same as which of the following?

x = 10 + 12 - 7

x = 10 + 12 + 7

x = 17 + 19

x = 70 + 84

When the 7 crosses over to the other side it becomes - 7

5 .

What is the value of c in the following equation: 4c = 2c + 75?

37.5

150

2c = 75

6 .

4(a + 7) = 40 is the same as which of the following?

4 - a - 7 = 40

4 - a + 7 = 40

4 + a + 7 = 40

4a + 28 = 40

Multiply the 4 (outside of the brackets) with both the a and the 7 (inside the brackets)

7 .

What is the value of f in the following equation: 7(f - 5) = 4(f - 3.5)?

7(f - 5) = 4(f - 3.5) is the same as 7f - 35 = 4f - 14. f must equal 7

8 .

Look at this equation: 10 + 18 = 7x. Now decide which of the following is not correct.

7x = 10 + 18

7x = 10 - 18

7x = 28

x = 4

First get the letter x onto the left hand side and then, in stages, break down its value

9 .

2x + 3y = 3y + 7 is the same as which of the following?

2x = 6y + 7

2x = 7

y = 2x - 7

y = 2x + 7

When + 3y crosses over to the other side it becomes - 3y and cancels out the 3y that was already on that side

10 .

What is the value of d in the following equation: 13d + 8 = 7d + 3d + 35?

'Write it down and work it out'. There is no alternative to a step by step approach!

You can find more about this topic by visiting BBC Bitesize - Equations

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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