Variables on Both Sides

≈ 25 min

When the variable appears on both sides, first gather all variable terms on one side and all constants on the other.

Worked example. Solve $7x - 5 = 2x + 20$ .

7x - 5 = 2x + 20

5x - 5 = 20 \qquad \text{(subtract } 2x\text{)}

5x = 25 \qquad \text{(add 5)}

x = 5 \qquad \text{(divide by 5)}

Check: LHS $= 7(5) - 5 = 30$ ; RHS $= 2(5) + 20 = 30$ ✓

Tip: move the smaller variable term — it keeps the coefficient positive and the arithmetic friendly.

Solve for $x$ : $7x - 5 = 2x + 20$

Solve and answer in the form x=…: $4x + 9 = x - 6$

For $9x - 7 = 4x + 18$ , which move correctly gathers the variable terms?

Add $4x$ to both sides

Subtract $4x$ from both sides

Subtract $9x$ from the left side only

Divide both sides by $x$

Solve for $x$ : $6x + 2 = 2x + 18$