Two-Step Equations
Grades 7–9 Algebra Equations
3x + 4 = 19 has two operations on x: multiplied by 3,
then 4 added. To undo, go backwards — undo the
addition first, then the multiplication. Think of unwrapping a gift:
outer layer first.
3x + 4 = 19
3x + 4 − 4 = 19 − 4 ← undo the +4 first
3x = 15
3x ÷ 3 = 15 ÷ 3 ← now undo the ×3
x = 5
Check: 3·(5) + 4 = 15 + 4 = 19 ✓
Variables on the right are fine too
24 = 7x − 4
24 + 4 = 7x − 4 + 4 ← undo the −4
28 = 7x
28 ÷ 7 = x
x = 4
Watch out
In
2x + 6 = 20, don't divide everything by 2
first — x + 6 = 10 is wrong (the 6 wasn't multiplied).
Strip the outside layer: subtract 6, then divide by 2.
The order mnemonic
Order of operations says do them as: parentheses → exponents
→ multiply/divide → add/subtract. Solving runs it
in reverse: peel off add/subtract first, then
multiply/divide.
Practice — solve each
2x + 6 = 14
5n − 3 = 22 — solve step by step:
Add 3 to both sides: 5n =
Divide by 5: n =
30 = 4y + 6
2x − 7 = −13
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