One-Step Equations
Grades 6–8 Algebra Equations
An equation is a balance scale: whatever is on the left equals whatever is on the right. To find the variable, undo what's been done to it — and whatever you do to one side, you must do to the other.
Undo + with −, undo × with ÷
x + 7 = 12
x + 7 − 7 = 12 − 7 ← subtract 7 from BOTH sides
x = 5
Check: 5 + 7 = 12 ✓
3x = 21
3x ÷ 3 = 21 ÷ 3 ← divide BOTH sides by 3
x = 7
Check: 3·(7) = 21 ✓
The four opposites
x + a = b→ subtract ax − a = b→ add aa·x = b→ divide by ax/a = b→ multiply by a
Always check
Plugging your answer back into the original equation takes five
seconds and catches most mistakes. It's the cheapest insurance in
math — build the habit now.
Practice — solve each
x + 4 = 13
y − 8 = −2
7n = 35
m/3 = 9 — solve in two steps:
Multiply both sides by 3: m = 9 ×
So m =
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