Practice Solution Set in Math

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

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Quick Recap

The complete set of all values that satisfy a given equation or inequality — it may be empty, finite, or infinite.

Not just one answer, but ALL answers that work — an inequality like x>3x > 3 has infinitely many.

Showing a random 20 of 50 problems.

Example 1

easy
Write the solution set of 3x=123x=12.

Example 2

easy
Write the solution set of x2=0x^2=0.

Example 3

hard
Find the solution set of ∣x−3∣≤4|x-3|\le 4.

Example 4

easy
Write the solution set of x2=9x^2=9.

Example 5

medium
Solve the compound condition −1≤x<3-1\le x<3 and describe its solution set.

Example 6

challenge
Find the solution set of x3=xx^3=x.

Example 7

medium
Find the solution set of x(x−2)(x+5)=0x(x-2)(x+5)=0.

Example 8

hard
Find the solution set of x−1x+2=0\frac{x-1}{x+2}=0.

Example 9

medium
Write the solution set of ∣x∣=4|x|=4.

Example 10

challenge
For what values of kk does x2=kx^2=k have a solution set with exactly one element (over the reals)?

Example 11

easy
What is the solution set of ∣x∣=0|x|=0?

Example 12

medium
Find the solution set of x2−4=0x^2-4=0.

Example 13

easy
Write the solution set of x+2=2x+2=2.

Example 14

hard
Find the solution set of x2−5x+6≤0x^2-5x+6\le 0.

Example 15

challenge
Find the solution set of 1x−2=1x−2\frac{1}{x-2}=\frac{1}{x-2}, noting any excluded value.

Example 16

medium
Write the solution set of −3<x≤2-3<x\le 2 in interval notation.

Example 17

hard
What is the solution set of x2+x+1=0x^2+x+1=0 over the reals?

Example 18

medium
Find the solution set of ∣x∣<3|x|<3.

Example 19

medium
Express the solution set of 1≤x<61\le x<6 in interval and set-builder form.

Example 20

hard
State the solution set of sin⁡x=2\sin x=2.
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