💡 Two-Step vs One-Step
One-step equations need just one operation. Two-step equations need two operations in a specific order: always undo addition or subtraction first, then undo multiplication or division. Think of it as "peeling an onion" — remove the outer layer first!
A two-step equation combines two operations on the variable x — typically addition or subtraction paired with multiplication or division.
Example: 2x + 3 = 11 — x is first multiplied by 2, then 3 is added. You undo both operations, but in reverse order.
→ x = 5
→ Step 2: divide by 2
→ x = 4
In 2x + 3 = 11, x has two things done to it: multiplied by 2 AND added 3. You must undo both.
Subtract 3 from both sides → 2x = 8
This removes the +3 "outer layer."
Divide both sides by 2 → x = 4
This removes the ×2 "inner layer." ✅
In the equation 3x − 5 = 13, what are the two operations on x? Which do you undo first?
both operations
Undo + or −
Undo × or ÷
Think of building a sandwich: multiplication "wraps" x first, then addition is the "outer layer." To undo it, peel the outer layer first (addition/subtraction), then unwrap the inner layer (multiplication/division).
This is the reverse of the order of operations (PEMDAS goes × before +, so we undo + before ×).
| Step | What To Do | Example | Result |
|---|---|---|---|
| Step 1 | Undo + or − (Add or Subtract) | 2x + 3 = 11 → −3 | 2x = 8 |
| Step 2 | Undo × or ÷ (Multiply or Divide) | 2x = 8 → ÷2 | x = 4 |
🔑 Memory Trick — "Socks Before Shoes"
When getting dressed, you put socks on before shoes. To undress, you take shoes off before socks — reverse order!
In algebra: the equation was built with × first then +. So to undo it: + first, then ×. Always reverse the order of operations!
2(4) + 3 = 8 + 3 = 11 ✅
Solve 3x + 4 = 16. (Step 1: subtract 4 from both sides → Step 2: divide by 3)
Solve 4x − 9 = 23. (Step 1: add 9 to both sides → Step 2: divide by 4)
The steps are exactly the same — but when you divide both sides by a negative number, a negative divided by a negative = positive!
Example: −6 ÷ −3 = +2
When you divide both sides by a negative coefficient:
Negative ÷ Negative = Positive (−6 ÷ −3 = +2)
Positive ÷ Negative = Negative (+10 ÷ −2 = −5)
The two steps work exactly the same — just apply sign rules carefully in Step 2!
−3x ÷ (−3) = −6 ÷ (−3) = +2 ✅
Negative ÷ negative = positive.
−5x ÷ (−5) = 20 ÷ (−5) = −4 ✅
Positive ÷ negative = negative.
Step 1: subtract 10 → −2x = −6
Step 2: ÷(−2) → x = −6÷(−2) = +3 ✅
Solve −4x + 8 = 0. (Step 1: subtract 8 → Step 2: divide by −4 — what sign is the answer?)
Example 1: a=2, b=3, c=11 → x=4 | Example 2: a=5, b=−7, c=18 → x=5 | Example 3: a=−3, b=6, c=0 → x=2