Solve linear equations in one variable

Discover

A pizza party costs 40 dollars plus 12 dollars per pizza, and the total is 100 dollars. Which equation fits?

$40 + 12p = 100$
$12 + 40p = 100$

Key idea

Equivalent equations have the same solutions.

To solve a linear equation, make equivalent equations: add or subtract the same amount on both sides, multiply or divide both sides by the same non-zero number, distribute, collect like terms. Stop when

x

is alone.

Worked example

Solve $5x + 3 = 2x + 15$ .

3x + 3 = 15

Subtract 2x.

3x = 12

Subtract 3.

x = 4

Divide by 3.

Your turn, guided

Your turn: $3(x + 2) = 21$ . Find $x$ .

x = 5

Divide by 3: x + 2 = 7.

Practice ★

Solve $3x + 3 = -18$ . $x = \;?$
Solve $8x + 14 = -26$ . $x = \;?$

Solve $4x + 8 = 3x + 9$ . $x = \;?$

Watch out!

Practice ★★

Solve $6(x + 4) = 30$ . $x = \;?$
Solve $3(x + 4) = 33$ . $x = \;?$

Exit ticket

Three questions to check you have got it.

Solve $3x + 3 = -18$ . $x = \;?$
Solve $8x + 14 = -26$ . $x = \;?$
Solve $4x + 4 = 32$ . $x = \;?$

Summary card

Linear equations

Do the same to both sides until $x$ is alone.

Watch out: distribute to every term.

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