Simplify expressions using combining like terms and the distributive property. | Linear equations in one variable | SAT Math

Distribute first, then combine like terms to simplify an expression before solving.

核心知识

Before solving, simplify each side: distribute to remove parentheses, then combine terms that share the same variable (or are both constants).

深入理解

The distributive property says $𝑎 (𝑏 + 𝑐) = 𝑎 𝑏 + 𝑎 𝑐$ . On the SAT, you'll use this to clear parentheses before doing anything else. Pay close attention to distributing negative signs — $- (3 𝑥 - 2)$ becomes $- 3 𝑥 + 2$ , not $- 3 𝑥 - 2$ .

Like terms share the same variable raised to the same power. So $5 𝑥$ and $- 2 𝑥$ are like terms (combine to $3 𝑥$ ), but $5 𝑥$ and $5 𝑥 2$ are not. Constants like $7$ and $- 3$ are also like terms.

Simplifying first often cuts a problem in half. An equation like $2 (𝑥 + 4) + 3 𝑥 = 28$ looks like it has many moving parts, but after distributing and combining, it's just $5 𝑥 + 8 = 28$ — a basic two-step equation.

分步讲解

Apply the distributive property to remove all parentheses.
Identify like terms on each side of the equation.
Combine like terms (add or subtract their coefficients).
Proceed to solve the simplified equation.

常见误解

Dropping the sign when distributing a negative: $- 2 (𝑥 - 5)$ is $- 2 𝑥 + 10$ , not $- 2 𝑥 - 10$ .
Combining unlike terms — for example, adding $3 𝑥 + 4$ to get $7 𝑥$ instead of leaving them separate.
Only distributing to the first term inside the parentheses and ignoring the rest.

题目

示例解析

Which expression is equivalent to $3 (2 𝑥 - 4) + 5 𝑥 - 1$ ?

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