Practice Balance Principle in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The rule that any operation applied to one side of an equation must also be applied to the other side to preserve equality.

An equation is like a balanced scaleβ€”add weight to both sides equally.

Showing a random 20 of 50 problems.

Example 1

easy
What operation undoes 'add 1212'?

Example 2

easy
Solve 2x=102x = 10.

Example 3

hard
Which is the FIRST step you should take to solve x2+6=10\frac{x}{2} + 6 = 10 using the balance principle?

Example 4

easy
Solve x+10=10x + 10 = 10.

Example 5

easy
Solve x+7=15x + 7 = 15 using the balance principle.

Example 6

hard
Solve 5(xβˆ’2)=3(x+4)5(x - 2) = 3(x + 4).

Example 7

hard
Solve 23x+4=12x+7\frac{2}{3}x + 4 = \frac{1}{2}x + 7.

Example 8

easy
Solve 7x=567x = 56.

Example 9

easy
To keep x=7x = 7 true after adding 33 to the left, what must you do to the right?

Example 10

easy
Solve x4=5\frac{x}{4} = 5.

Example 11

medium
Solve 2(x+4)=222(x + 4) = 22.

Example 12

hard
Solve 7βˆ’2(3βˆ’x)=5xβˆ’97 - 2(3 - x) = 5x - 9.

Example 13

hard
Solve for hh in the formula A=12bhA = \frac{1}{2}bh.

Example 14

challenge
For what value of cc does 2x+c=2x+72x + c = 2x + 7 hold for ALL xx? Explain using balance.

Example 15

easy
Solve 3x=183x = 18.

Example 16

medium
Solve 3xβˆ’4=143x - 4 = 14 using the balance principle, showing all steps.

Example 17

medium
Solve 4(xβˆ’1)=124(x - 1) = 12.

Example 18

challenge
Solve for xx: 3x+2xβˆ’1=5\frac{3x + 2}{x - 1} = 5, xβ‰ 1x \ne 1.

Example 19

medium
Solve 5x+8=335x + 8 = 33, showing each balanced step.

Example 20

medium
From 2x+3=92x + 3 = 9, a student subtracts 33 to get 2x=92x = 9. What went wrong, and what is correct?
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