Solving an equation means finding the value of x that makes it true. The key idea is simple: an equation is like a balance scale. Whatever you do to one side, you must do to the other side. Your goal is to get x alone.
You do that by using inverse operations — the opposite of whatever operation is being applied to x.
Addition ↔ Subtraction
If x has + 5, subtract 5 from both sides
Multiplication ↔ Division
If x has × 3, divide both sides by 3
Watch the signs. A negative coefficient like −3x means x is being multiplied by −3. Dividing both sides by −3 flips the sign. Negative ÷ negative = positive. Positive ÷ negative = negative.
The 4-Step Order
Always follow this order when solving multi-step equations:
1
Parentheses first — distribute using the distributive property if there are parentheses
2
Get the variable on one side — combine like terms if needed
3
Undo addition and subtraction — move constants to the other side
4
Undo multiplication and division — isolate x completely
Worked Example — One-Step
Solve: x + 5 = −2
x + 5 = −2
x has +5 added to it — undo this by subtracting 5 from both sides
x + 5 − 5 = −2 − 5
x = −7
Check: substitute −7 back in → −7 + 5 = −2 ✓
Worked Example — Two-Step
Solve: −3x − 4 = 8
−3x − 4 = 8
Step 1: x has 4 subtracted from it — undo this by adding 4 to both sides
−3x − 4 + 4 = 8 + 4
−3x = 12
Step 2: x is being multiplied by −3 — undo this by dividing both sides by −3
−3x ÷ (−3) = 12 ÷ (−3)
x = −4
Check: −3(−4) − 4 = 12 − 4 = 8 ✓
Worked Example — Multi-Step with Parentheses
Solve: −3(x − 2) + 5 = 11
−3(x − 2) + 5 = 11
Step 1: Parentheses first — distribute −3 to both terms inside (watch the sign: −3 × −2 = +6)
−3x + 6 + 5 = 11
Step 2: Combine like terms on the left side (6 + 5 = 11)
−3x + 11 = 11
Step 3: Undo adding 11 by subtracting 11 from both sides
−3x = 0
Step 4: Undo multiplying by −3 by dividing both sides by −3
x = 0
Check: −3(0 − 2) + 5 = 6 + 5 = 11 ✓
GED Strategy: Always check your answer by substituting it back into the original equation. If both sides are equal, you're right. This takes 10 seconds and catches most errors.
Common mistakes to watch for:
• Distributing a negative — remember −3(x − 2) = −3x + 6, not −3x − 6
• Doing only one side — whatever you do to the left, do to the right
• Sign errors when dividing by a negative number
Reference
GED Formula Sheet
All formulas available on the real test — opens in a new tab