Solving One-Variable Linear Equations
Key rules, steps, and traps for isolating a variable in PSAT linear equations.
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Questions Covered in This Set
10 cards to master
Golden rule of equation solving
Whatever you do to one side, do to the other side — adding, subtracting, multiplying, or dividing by the same nonzero number preserves equality.
The 5-step order of moves
1) Clear fractions, 2) Distribute, 3) Combine like terms on each side, 4) Move variables to one side and constants to the other, 5) Divide by the coefficient.
Solve 3x + 5 = 20
Subtract 5: 3x = 15. Divide by 3: x = 5. (Check: 3(5)+5 = 20 ✓)
Solve 7x - 4 = 2x + 11
Subtract 2x: 5x - 4 = 11; add 4: 5x = 15; x = 3.
Which side should the variable terms go to?
The side that keeps the coefficient positive — fewer sign errors.
What does -2(x + 5) expand to?
-2x - 10, NOT -2x + 10. Always carry the sign with the number.
How do you clear fractions like (x/3) + (x-1)/4 = 5?
Multiply every term on both sides by the least common denominator (12): 4x + 3(x-1) = 60 → 7x = 63 → x = 9.
When is cross-multiplication allowed?
Only when each side is a single fraction, e.g. (2x+1)/5 = (x-4)/3 → 3(2x+1) = 5(x-4).
Biggest PSAT trap with linear equations
The question asks for an expression (like 3x or 4x), not x. Circle what's being asked before solving.
How do you solve (2/3)x = 8?
Multiply both sides by the reciprocal 3/2: x = 12.
