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 $x > 3$ has infinitely many.

Showing a random 20 of 50 problems.

Example 1

easy

Write the solution set of

3x=12

Example 2

easy

Write the solution set of

x^2=0

Example 3

hard

Find the solution set of

|x-3|\le 4

Example 4

easy

Write the solution set of

x^2=9

Example 5

medium

Solve the compound condition

-1\le x<3

and describe its solution set.

Example 6

challenge

Find the solution set of

x^3=x

Example 7

medium

Find the solution set of

x(x-2)(x+5)=0

Example 8

hard

Find the solution set of

\frac{x-1}{x+2}=0

Example 9

medium

Write the solution set of

|x|=4

Example 10

challenge

For what values of

k

does

x^2=k

have a solution set with exactly one element (over the reals)?

Example 11

easy

What is the solution set of

|x|=0

Example 12

medium

Find the solution set of

x^2-4=0

Example 13

easy

Write the solution set of

x+2=2

Example 14

hard

Find the solution set of

x^2-5x+6\le 0

Example 15

challenge

Find the solution set of

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

, noting any excluded value.

Example 16

medium

Write the solution set of

-3<x\le 2

in interval notation.

Example 17

hard

What is the solution set of

x^2+x+1=0

over the reals?

Example 18

medium

Find the solution set of

|x|<3

Example 19

medium

Express the solution set of

1\le x<6

in interval and set-builder form.

Example 20

hard

State the solution set of

\sin x=2

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Related Concepts

Solution Concept Interval Notation Empty Set