Unknowns on both sides

Objective. Collect unknowns and constants to solve balanced equations.

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2. Worked example
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Learn: the key idea

Unknowns on both sides equations have the variable appearing on each side, so the first step is to collect all the unknown terms onto one side and all the constant numbers onto the other, keeping the equation balanced throughout. For 5x + 3 = 2x + 15, subtract 2x from both sides to get 3x + 3 = 15, then subtract 3 to get 3x = 12, giving x = 4. It usually helps to move the smaller unknown term so the remaining coefficient stays positive, avoiding extra negative sign errors.

Worked example

Solve the equation with unknowns on both sides 7x − 4 = 3x + 16.

1 $Subtract 3x from both sides: 4x - 4 = 16$
2 $Add 4 to both sides: 4x = 20$
3 $Divide both sides by 4: x = 5$
4 $Check: 7(5) - 4 = 31 and 3(5) + 16 = 31$

Answer: x = 5

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Common mistake. Pupils sometimes subtract the unknown terms but forget to also apply the same operation to the constants on that side, turning 5x + 3 = 2x + 15 into 3x + 3 = 15 correctly but then mishandling the next step as 3x = 15 instead of 3x = 12.

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