Equations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Equations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A mathematical statement that two expressions are equal, connected by an equals sign ( $=$ ). Equations assert a relationship between quantities and can be solved to find the values of unknown variables that make the statement true.

A balanced scale: both sides must weigh the same. Solve by keeping balance.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: An equation claims two expressions are equal and asks which values keep them equal.

Common stuck point: The procedure for equations is the easy part; the trap is operating on one side only. Asking "Are two expressions joined by $=$ with an unknown I'm asked to make the statement true?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Are two expressions joined by $=$ with an unknown I'm asked to make the statement true?

Worked Examples

Example 1

easy

x = 4

a solution of

2x - 3 = 5

Answer

Yes,

x = 4

is a solution.

First step

Substitute

x = 4

into the left side:

2(4) - 3 = 8 - 3 = 5

Full solution

2
Compare with the right side: $5 = 5$ ✓.
3
Since both sides are equal, $x = 4$ is a solution.

An equation asserts that two expressions are equal. A value is a solution if substituting it makes both sides equal. Always check by plugging the value back in.

Example 2

medium

Solve

\frac{x}{4} + 3 = 7

Example 3

medium

Solve

2x + 5 = 17

Example 4

medium

Solve

-2x + 7 = 1

Example 5

hard

Solve

4(x + 1) = 2(x + 5)

Example 6

hard

A taxi ride costs \$3 plus \$2 per mile. The total bill is \$17. How many miles?

Example 7

challenge

Solve

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

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Solve

x + 9 = 15

Example 2

hard

Which of these is an equation and which is an expression? (a)

3x + 7

(b)

3x + 7 = 19

Example 3

easy

Solve:

x + 5 = 12

Example 4

easy

Solve:

3x = 21

Example 5

easy

x = 3

a solution of

2x + 1 = 7

Example 6

easy

Solve:

x - 4 = -9

Example 7

easy

Solve:

2x + 3 = 11

Example 8

easy

What value of

x

makes

x = x + 1

true?

Example 9

easy

Solve:

\frac{x}{4} = 3

Example 10

easy

Translate 'a number plus

7

equals

20

' into an equation.

Example 11

medium

Solve:

3(x - 2) = 9

Example 12

medium

Solve:

5x - 3 = 2x + 9

Example 13

medium

Solve:

\frac{x+1}{3} = 4

Example 14

medium

Solve for

x

ax = b

(with

a \ne 0

Example 15

medium

How many solutions does

2(x + 1) = 2x + 2

have?

Example 16

medium

A number tripled and decreased by

4

17

. Find it.

Example 17

medium

Solve:

0.5x + 2 = 6

Example 18

challenge

Solve for

x

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

Example 19

challenge

Solve:

\sqrt{x + 3} = x - 3

Example 20

challenge

For what value of

k

does

hard

The sum of two consecutive integers is

73

. Find the smaller one.

Example 39

hard

Solve

6 - (2x - 1) = 3x + 2

← Back to Equations Formula Explained Practice Mode

Related Concepts

Expressions Equal Solving Linear Equations Inequalities

Background Knowledge

These ideas may be useful before you work through the harder examples.

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