SAT Linear Equations in One Variable study notes

An equation is a balance: every move you make on one side has to happen on the other. When fractions or parentheses appear, clear or expand them carefully before collecting x terms. Then check the value in the original equation, not just the simplified one.

Worked example

Solve 2(x − 3)/5 + (x + 1)/3 = 5.

Multiply through by 15: 6(x − 3) + 5(x + 1) = 75. Distribute to get 11x − 13 = 75, so x = 8. Check: 2(5)/5 + 9/3 = 2 + 3 = 5.

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