Linear Equations • Topic 4 of 6

Variables on Both Sides

When the variable appears on both sides, first gather the variable terms on one side and the constants on the other by adding or subtracting. For 5x + 2 = 3x + 10, subtract 3x to get 2x + 2 = 10, then solve normally. It is usually easiest to move the smaller variable term so the coefficient stays positive. After collecting terms you are left with a one- or two-step equation. These problems test whether you can keep an equation balanced while moving terms across the equals sign, a skill the SAT uses in systems and word problems.

✅ Solved examples

1. Solve 5x + 2 = 3x + 10.
Subtract 3x: 2x + 2 = 10; subtract 2: 2x = 8; divide: x = 4.
2. Solve 7x = 2x + 15.
Subtract 2x: 5x = 15; divide: x = 3.
3. Solve 4x − 3 = x + 9.
Subtract x: 3x − 3 = 9; add 3: 3x = 12; divide: x = 4.
4. Solve 6x + 1 = 2x + 13.
Subtract 2x: 4x + 1 = 13; subtract 1: 4x = 12; divide: x = 3.

✏️ Practice — try these, take hints as needed

1. Solve 6x + 4 = 2x + 20.
Subtract 2x.
4x + 4 = 20.
Solve the two-step equation.
4.
2. Solve 8x = 3x + 25.
Subtract 3x.
5x = 25.
Divide.
5.
3. Solve 5x − 2 = 2x + 7.
Subtract 2x.
3x − 2 = 7.
Add 2, divide by 3.
3.
4. Solve 9x + 1 = 4x + 26.
Subtract 4x.
5x + 1 = 26.
Subtract 1, divide by 5.
5.
5. Solve 3x + 8 = 7x.
Subtract 3x from both sides.
8 = 4x.
Divide by 4.
2.

📝 Topic test — 8 questions

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