Practice Algebraic Manipulation in Math

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

Quick Recap

Algebraic manipulation is the process of rewriting expressions or equations into equivalent forms to reveal structure or solve for unknowns.

It is like rearranging a sentence without changing its meaning.

Showing a random 20 of 50 problems.

Example 1

medium
Expand and simplify (x−3)(x+5).

Example 2

easy
Expand 3(2x−4).

Example 3

medium
Simplify x2−9x−3 for x≠3.

Example 4

medium
Solve for r: C=2πr.

Example 5

medium
Expand and simplify (x+2)(x+3).

Example 6

hard
Solve 2x−1x+3=3 for x.

Example 7

easy
Expand −(x−4).

Example 8

challenge
Solve for x: 1x+12=34.

Example 9

medium
Factor x2−5x−24.

Example 10

easy
Solve 3x=21.

Example 11

medium
Rearrange A=12bh to solve for b.

Example 12

easy
Simplify 3x+2x.

Example 13

easy
Simplify 2(x+3)−x.

Example 14

medium
Simplify x+3x as far as possible.

Example 15

medium
Solve x+42=7.

Example 16

hard
Simplify x2−x−6x2−9 for x≠±3.

Example 17

easy
Simplify 5x−3+2x+7.

Example 18

medium
Solve 5x−2=3x+8.

Example 19

medium
Solve 2x+3=11.

Example 20

medium
Solve 2x−13=5.