学习 · 代数1

Linear Equations: The Five-Step Method That Solves Every "Find x"

Every solve-for-x problem on the Algebra 1 Test Out 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.

8 分钟Michigan Standards 2A,5A,5B代数1

One template solves them all

Every “solve for x” problem on the Michigan Algebra 1 Test Out — 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
  1. Distribute — clear any parentheses
  2. Combine — collect like terms on each side
  3. Move variables to one side, numbers to the other
  4. Divide by the coefficient of x
  5. Check — substitute back into the original

The balance metaphor

2x + 517whatever you do to ONE side, do to the OTHER
Equation = balanced scale. Subtract 5 from both sides → 2x = 12. Divide by 2 → x = 6. Check: 2(6)+5 = 17 ✓

Type 1: Two-step equation

2x + 5 = 172x + 5 − 5 = 17 − 52x = 12x = 6Subtract first (constants), then divide (coefficient).

Type 2: Distributive property first

When you see parentheses, distribute first — then continue normally.

4(x − 3) = 2x + 64x − 12 = 2x + 64x − 2x = 6 + 122x = 18x = 9
Try a distributive equation
Solve for x: 4(x - 3) = 2x + 6

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 − bx = (c − b) / aTreat a, b, c as numbers you simply don't know yet. The procedure is identical.
Solve a literal equation
Solve for x: ax + b = c

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 Test Out often gives you four numbers, only one of which checks.

Check yourself

Quick check #1
Solve for x: 3(x − 2) = 15.
Quick check #2
What is the FIRST step in solving 2x + 4 = 5x − 11?