A two-step equation needs two inverse operations to get the variable on its own, such as 3c − 15 = −45 or x/4 + 3 = 8. The method is always the same: undo the addition or subtraction first, then undo the multiplication or division, doing the same thing to both sides each time. Then substitute your answer back in to check it. This guide walks through the method, solves eight examples including negatives and fractions, and ends with practice questions and answers. When you want quick-fire practice, play Solve for X; to check any linear equation step by step, use the equation solver.
Find the constant that is added to or subtracted from the variable term, and undo it on both sides.
Find the coefficient multiplying (or dividing) the variable, and undo it on both sides.
Check by putting your answer back into the original equation.
Why this order? The equation was built by doing the operations in order-of-operations sequence: multiply first, then add. Solving reverses that sequence, like taking off your shoes before your socks. If order of operations feels shaky, that page is a quick refresher.
Undo the subtraction: add 15 to both sides. 3c − 15 + 15 = −45 + 15, so 3c = −30.
Undo the multiplication: divide both sides by 3. c = −10.
Check: 3 × (−10) − 15 = −30 − 15 = −45. ✓
The most common slip here is writing −45 + 15 = −60. Adding a positive number to a negative one moves you towards zero, so the answer is −30. A number line helps until it is automatic.
Notice the sixth example, (x + 3)/2 = 9. The brackets mean the 3 was added before dividing, so here you undo the division first. The rule is not "always add first" but "undo the last operation that was done to x first".
| Equation | Step 1 | Step 2 | Answer |
|---|---|---|---|
| 2x + 5 = 17 | Subtract 5: 2x = 12 | Divide by 2 | x = 6 |
| 4y − 7 = 21 | Add 7: 4y = 28 | Divide by 4 | y = 7 |
| −5y + 8 = 23 | Subtract 8: −5y = 15 | Divide by −5 | y = −3 |
| 7 − 2n = 15 | Subtract 7: −2n = 8 | Divide by −2 | n = −4 |
| x/4 − 3 = 2 | Add 3: x/4 = 5 | Multiply by 4 | x = 20 |
| (x + 3)/2 = 9 | Multiply by 2: x + 3 = 18 | Subtract 3 | x = 15 |
| 0.5m + 1.5 = 4 | Subtract 1.5: 0.5m = 2.5 | Divide by 0.5 | m = 5 |
When the variable is multiplied by a negative number, divide by that negative number, sign included. In 7 − 2n = 15, the term is −2n, not 2n. After subtracting 7 you have −2n = 8, and dividing by −2 gives n = −4. Check: 7 − 2 × (−4) = 7 + 8 = 15. ✓
A positive divided by a negative is negative: 8 ÷ (−2) = −4.
A negative divided by a negative is positive: −30 ÷ (−3) = 10.
If the equation is −x = 6, that is −1 × x = 6, so x = −6.
A coefficient such as 2/3 is undone by multiplying by its reciprocal, 3/2. For (2/3)x + 4 = 10: subtract 4 to get (2/3)x = 6, then multiply both sides by 3/2 to get x = 9. Check: (2/3) × 9 = 6, and 6 + 4 = 10. ✓
Another route is to clear the fraction first by multiplying every term by the denominator: 3 × [(2/3)x + 4 = 10] gives 2x + 12 = 30, then 2x = 18 and x = 9. Both routes give the same answer; choose whichever keeps the numbers whole. Simplifying fractions helps keep the working tidy.
"A taxi charges a $3 pick-up fee plus $2 per mile. The fare was $19. How far was the ride?" Let m be the miles: 2m + 3 = 19. Subtract 3 to get 2m = 16, divide by 2 to get m = 8 miles. Check: 2 × 8 + 3 = 19. ✓
Most word problems of this kind have a fixed amount (the constant) and a rate (the coefficient). Name the unknown, write the equation, then solve with the same two steps.
5x + 2 = 37
3a − 8 = −20
−4k + 6 = −10
x/3 + 7 = 12
9 − 3p = 0
(y − 5)/4 = 3
Answers: 1) x = 7, 2) a = −4, 3) k = 4, 4) x = 15, 5) p = 3, 6) y = 17. If you got one wrong, substitute your answer into the original equation to see where the arithmetic slipped. For speed, the Solve for X game gives you a stream of one- and two-step equations against the clock.
An equation that needs two inverse operations to isolate the variable, usually one addition or subtraction and one multiplication or division, such as 2x + 5 = 17.
Undo the last operation that was applied to the variable. In 3c − 15 = −45 that is the subtraction, so add 15 to both sides first, then divide by 3.
c = −10. Adding 15 to both sides gives 3c = −30, and dividing by 3 gives −10. Check: 3 × (−10) − 15 = −45.
Substitute the value back into the original equation. If both sides are equal, the answer is right.
Move all the variable terms to one side first, for example by subtracting the smaller x term from both sides, and it becomes a two-step equation. The equation solver shows each step.
Undo addition or subtraction, then undo multiplication or division, doing the same to both sides, and always check by substitution. With a dozen practice questions the method becomes automatic. Keep it sharp with Solve for X, and use the equation solver when you want to see every step.