Practice Isolating Variable 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

Rearranging an equation by applying inverse operations until the variable stands alone on one side.

Peel away everything around xx until only xx remains: x=x = answer.

Showing a random 20 of 50 problems.

Example 1

easy
Isolate xx: x3=6\frac{x}{3}=6.

Example 2

medium
Isolate xx: 3x+7=193x+7=19.

Example 3

medium
Solve for bb: A=a+b2A=\frac{a+b}{2}.

Example 4

easy
Isolate xx: 4x=204x=20.

Example 5

hard
Solve for xx in terms of a,ba, b: xโˆ’ab=x+ba\frac{x - a}{b} = \frac{x + b}{a} (a,bโ‰ 0a, b \neq 0, aโ‰ ba \neq b).

Example 6

medium
Solve for yy: 3xโˆ’4y=123x - 4y = 12.

Example 7

medium
Solve for xx: 5(2x+1)โˆ’4=215(2x + 1) - 4 = 21.

Example 8

easy
Solve for xx: x+12=5x + 12 = 5.

Example 9

hard
Solve for xx: 2xโˆ’13=16\frac{2}{x} - \frac{1}{3} = \frac{1}{6} (with xโ‰ 0x \neq 0).

Example 10

easy
Solve for xx: 2x3=8\frac{2x}{3} = 8.

Example 11

easy
Isolate xx: โˆ’x=5-x=5.

Example 12

easy
Solve for xx: 6x=426x = 42.

Example 13

medium
Isolate xx: x+42=6\frac{x+4}{2}=6.

Example 14

medium
Solve for rr: C=2ฯ€rC=2\pi r.

Example 15

challenge
Solve for xx: ax+b=cax+b=c (with aโ‰ 0a\ne0), in terms of a,b,ca,b,c.

Example 16

challenge
Solve for tt: s=ut+12at2s=ut+\frac{1}{2}at^2 is hard; instead solve v=u+atv=u+at for tt.

Example 17

medium
Solve for xx: 4x+7=2x+194x + 7 = 2x + 19.

Example 18

medium
Isolate xx: 5xโˆ’3=2x+95x-3=2x+9.

Example 19

easy
Isolate xx in xโˆ’7=3x - 7 = 3.

Example 20

easy
Isolate xx: x+12=2x+\frac{1}{2}=2.
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