Multi-Step Linear Equations

Before isolating x, you often need to simplify each side of the equation by combining like terms. Like terms have the same variable raised to the same power: - 3x and 5x are like terms → 3x + 5x = 8x - 7 and -2 are like terms → 7 + (-2) = 5 - 3x and 3x^2 are NOT like terms

Example: Solve 4x + 3 + 2x = 21

When an equation contains parentheses, use the distributive property to expand them first: [formula] Careful with negative signs in front of parentheses: [formula] [formula]

Example: Solve 3(x + 4) = 27

When x appears on both sides of the equation, collect all x-terms on one side and all constants on the other. Strategy: move the smaller x-term to the side with the larger x-term to avoid negative coefficients (though negatives still work!).

Example: Solve 5x + 3 = 2x + 18

When you see a multi-step equation on the SAT, don't rush. Take 5 seconds to scan the whole equation before starting. If there are parentheses, distribute first. If there are like terms, combine them. Working neatly prevents sign errors — the #1 source of mistakes on these problems.