Linear Equations: The Five-Step Method That Solves Every “Find x”
Every solve-for-x problem on the Algebra 1 CBE comes down to the same five moves — distribute, combine, isolate, divide, check. Master the order and you'll handle one-step through both-sides equations on autopilot.
One template solves them all
Every “solve for x” problem on the Texas Algebra 1 CBE — whether it has parentheses, fractions, decimals, or variables on both sides — reduces to the same five-step recipe. Learn the order once, and you'll never get stuck on a linear equation again.
The five-step method
- Distribute — clear any parentheses
- Combine — collect like terms on each side
- Move variables to one side, numbers to the other
- Divide by the coefficient of x
- Check — substitute back into the original
The balance metaphor
Type 1: Two-step equation
2x + 5 = 17 2x + 5 − 5 = 17 − 5 2x = 12 x = 6 Subtract first (constants), then divide (coefficient).
Type 2: Distributive property first
When you see parentheses, distribute first — then continue normally.
4(x − 3) = 2x + 6 4x − 12 = 2x + 6 4x − 2x = 6 + 12 2x = 18 x = 9
Type 3: Literal equations (solve in terms of letters)
Same five steps — but instead of a number, you isolate one letter on its side.
ax + b = c (solve for x) ax = c − b x = (c − b) / a Treat a, b, c as numbers you simply don't know yet. The procedure is identical.
The four traps
Common mistakes
- Forgetting to distribute through subtraction: −3(x − 2) = −3x + 6, not −3x − 6.
- Variables on both sides: move them all to one side first; then proceed.
- Fractions: multiply both sides by the LCD to clear them in one step.
- Always check by substituting your answer into the original equation.
3-second recap
- Distribute → combine → isolate → divide → check.
- Whatever you do to one side, do to the other (the balance rule).
- Variables on both sides? Move them to one side first.
- Fractions? Multiply through by the LCD.
- Always substitute back — the CBE often gives you four numbers, only one of which checks.