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

x=-2

a valid solution of

\log(x)=1

Example 2

easy

x=5

a solution of

x-2=4

Example 3

medium

After solving, a student claims

x=10

solves

\frac{x}{x-10}=1

. Verify.

Example 4

easy

x=9

a solution of

\sqrt{x}=3

Example 5

medium

Verify: is

(x,y)=(3,4)

a solution of

x^2+y^2=25

Example 6

medium

After solving

\sqrt{2x+1}=x-1

, candidates are

x=0

and

x=4

. Check each.

Example 7

easy

x=2

a solution of

x^2=4

Example 8

medium

(x,y)=(0,0)

a solution of

y=x^2+1

Example 9

hard

For

\log_2(x-1)+\log_2(x+1)=3

, a candidate is

x=3

. Verify.

Example 10

easy

x=6

a solution of

x-3=2

Example 11

challenge

Suppose squaring gives candidates

x=2

and

x=-2

for

\sqrt{4-x^2}=x

. Which are valid?

Example 12

easy

Does

x=7

satisfy

2x+1=15

Example 13

medium

x=-1

a solution of

\frac{2}{x+1}=3

Example 14

easy

x=1

a solution of

2x+3=x+5

Example 15

challenge

For what value(s) of

x

is the proposed solution

x=4

valid in

\frac{1}{x-4}+\frac{1}{x}= \frac{1}{2}

Example 16

hard

(x,y)=(1,1)

a solution of

x^2+y^2=4

Example 17

medium

x=3

a solution of

\frac{x+1}{x-3}=2

Example 18

easy

x=4

a solution of

\frac{x}{2}=2

Example 19

medium

Solve

x^2=16

and verify both candidates.

Example 20

medium

x=3

a solution of

|x-1|=2

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Related Concepts

Evaluation Solution Concept Equivalence