Practice Checking Solutions in Math

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

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Quick Recap

Checking solutions means substituting candidate values back into the original condition to verify they satisfy it.

Treat your answer as a hypothesis and test it by substituting back into the original equation to verify.

Showing a random 20 of 50 problems.

Example 1

medium
Is x=−2x=-2 a valid solution of log⁡(x)=1\log(x)=1?

Example 2

easy
Is x=5x=5 a solution of x−2=4x-2=4?

Example 3

medium
After solving, a student claims x=10x=10 solves xx−10=1\frac{x}{x-10}=1. Verify.

Example 4

easy
Is x=9x=9 a solution of x=3\sqrt{x}=3?

Example 5

medium
Verify: is (x,y)=(3,4)(x,y)=(3,4) a solution of x2+y2=25x^2+y^2=25?

Example 6

medium
After solving 2x+1=x−1\sqrt{2x+1}=x-1, candidates are x=0x=0 and x=4x=4. Check each.

Example 7

easy
Is x=2x=2 a solution of x2=4x^2=4?

Example 8

medium
Is (x,y)=(0,0)(x,y)=(0,0) a solution of y=x2+1y=x^2+1?

Example 9

hard
For log⁡2(x−1)+log⁡2(x+1)=3\log_2(x-1)+\log_2(x+1)=3, a candidate is x=3x=3. Verify.

Example 10

easy
Is x=6x=6 a solution of x−3=2x-3=2?

Example 11

challenge
Suppose squaring gives candidates x=2x=2 and x=−2x=-2 for 4−x2=x\sqrt{4-x^2}=x. Which are valid?

Example 12

easy
Does x=7x=7 satisfy 2x+1=152x+1=15?

Example 13

medium
Is x=−1x=-1 a solution of 2x+1=3\frac{2}{x+1}=3?

Example 14

easy
Is x=1x=1 a solution of 2x+3=x+52x+3=x+5?

Example 15

challenge
For what value(s) of xx is the proposed solution x=4x=4 valid in 1x−4+1x=12\frac{1}{x-4}+\frac{1}{x}= \frac{1}{2}?

Example 16

hard
Is (x,y)=(1,1)(x,y)=(1,1) a solution of x2+y2=4x^2+y^2=4?

Example 17

medium
Is x=3x=3 a solution of x+1x−3=2\frac{x+1}{x-3}=2?

Example 18

easy
Is x=4x=4 a solution of x2=2\frac{x}{2}=2?

Example 19

medium
Solve x2=16x^2=16 and verify both candidates.

Example 20

medium
Is x=3x=3 a solution of ∣x−1∣=2|x-1|=2?
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