Two-step equations are the first place students meet the idea of undoing operations in reverse order. The variable was multiplied and then had a number added; to isolate it, you undo the addition first and the multiplication second.
DeltaMath randomizes the coefficients and constants, so the same skill can produce integers, negatives, fractions, and decimals. The steps never change.
How to solve it, step by step
Undo the addition or subtraction
Look at the constant on the same side as the variable. Add or subtract it from both sides so the variable term stands alone. For 3x − 7 = 11, add 7 to both sides: 3x = 18.
Undo the multiplication or division
Divide both sides by the coefficient (or multiply if the variable is divided). 3x = 18 → x = 6. If the variable is x/3, multiply both sides by 3.
Check by substituting back
Replace x with your answer in the original equation: 3(6) − 7 = 18 − 7 = 11 ✓. This takes ten seconds and catches sign errors before DeltaMath does.
Worked example
Solve −5x + 8 = 33.
- −5x + 8 = 33
- −5x = 25 (subtract 8 from both sides)
- x = 25 / (−5) (divide both sides by −5)
- x = −5
- Check: −5(−5) + 8 = 25 + 8 = 33 ✓
Answer x = −5
Solve x/4 − 3 = 2.
- x/4 = 5 (add 3 to both sides)
- x = 20 (multiply both sides by 4)
Answer x = 20
Mistakes DeltaMath marks wrong
- Dividing before subtracting, which forces you to divide every term and invites fraction mistakes.
- Losing the sign on a negative coefficient: 25 ÷ (−5) is −5, not 5.
- Subtracting the constant from only one side.
- Entering the answer as "x = 6" when the box only wants 6.
How to type the answer
- Enter only the value: 6, -5, 3/2, 2.5.
- Fractions are accepted with a slash; improper fractions are fine, mixed numbers are not.
- DeltaMath accepts equivalent forms (0.5 and 1/2) unless the problem says otherwise.