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 59 problems.

Example 1

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

Example 2

medium
Isolate xx: 2(x+3)=142(x+3)=14.

Example 3

medium
Solve for hh: V=Ο€r2hV = \pi r^2 h.

Example 4

easy
Isolate xx: x+8=15x+8=15.

Example 5

hard
Solve for rr: A=P(1+rt)A = P(1 + rt) (simple interest).

Example 6

challenge
Solve for xx: log⁑2(xβˆ’1)+log⁑2(x+1)=3\log_2(x - 1) + \log_2(x + 1) = 3.

Example 7

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

Example 8

hard
Solve for xx: 2(3xβˆ’1)βˆ’4(x+5)=62(3x - 1) - 4(x + 5) = 6.

Example 9

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

Example 10

medium
Solve for rr: C=2Ο€rC=2\pi r.

Example 11

easy
Isolate xx: 2x=72x=7.

Example 12

easy
Solve for xx: βˆ’3x=21-3x = 21.

Example 13

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

Example 14

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

Example 15

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

Example 16

easy
Fill in the blank so that the solution is x=6x = 6: x2+__=10\frac{x}{2} + \_\_ = 10.

Example 17

medium
Solve for xx: xβˆ’34=x+16\frac{x - 3}{4} = \frac{x + 1}{6}.

Example 18

medium
Solve for xx: 3(xβˆ’4)=183(x - 4) = 18.

Example 19

hard
Solve for xx: 2x+5=7\sqrt{2x + 5} = 7.

Example 20

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