Practice Algebraic Manipulation 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

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 (xโˆ’3)(x+5)(x - 3)(x + 5).

Example 2

easy
Expand 3(2xโˆ’4)3(2x - 4).

Example 3

medium
Simplify x2โˆ’9xโˆ’3\dfrac{x^2 - 9}{x - 3} for xโ‰ 3x \ne 3.

Example 4

medium
Solve for rr: C=2ฯ€rC = 2\pi r.

Example 5

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

Example 6

hard
Solve 2xโˆ’1x+3=3\dfrac{2x - 1}{x + 3} = 3 for xx.

Example 7

easy
Expand โˆ’(xโˆ’4)-(x - 4).

Example 8

challenge
Solve for xx: 1x+12=34\dfrac{1}{x} + \dfrac{1}{2} = \dfrac{3}{4}.

Example 9

medium
Factor x2โˆ’5xโˆ’24x^2 - 5x - 24.

Example 10

easy
Solve 3x=213x = 21.

Example 11

medium
Rearrange A=12bhA = \dfrac{1}{2}bh to solve for bb.

Example 12

easy
Simplify 3x+2x3x + 2x.

Example 13

easy
Simplify 2(x+3)โˆ’x2(x + 3) - x.

Example 14

medium
Simplify x+3x\dfrac{x+3}{x} as far as possible.

Example 15

medium
Solve x+42=7\dfrac{x + 4}{2} = 7.

Example 16

hard
Simplify x2โˆ’xโˆ’6x2โˆ’9\dfrac{x^2 - x - 6}{x^2 - 9} for xโ‰ ยฑ3x \ne \pm 3.

Example 17

easy
Simplify 5xโˆ’3+2x+75x - 3 + 2x + 7.

Example 18

medium
Solve 5xโˆ’2=3x+85x - 2 = 3x + 8.

Example 19

medium
Solve 2x+3=112x + 3 = 11.

Example 20

medium
Solve 2xโˆ’13=5\dfrac{2x - 1}{3} = 5.
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