Solving Two-Step Equations (Grades 6–7)
A two-step equation has two operations to undo, like 2x + 3 = 11.
Understanding solving two-step equations
Undo them in the reverse of the order they were done to x, always doing the same to both sides. In 2x + 3 = 11, x is multiplied by 2 and then 3 is added, so undo the adding first and the multiplying second. Brackets change the order: in 2(x + 3) = 14, the 3 is added first and the result is doubled, so there you undo the multiplying first. Peeling the equation back one layer at a time gets x alone.
Seeing it in action
Worked example
Solve 2x + 3 = 11.
Undo +3 first: 2x = 11 − 3 = 8.
Undo ×2: x = 8 ÷ 2 = 4. (Check: 2·4 + 3 = 11 ✓.)
Undo +3, then undo ×2.
Worked example 2: brackets
Solve 2(x + 3) = 14.
Here 3 is added inside the brackets first, and then the whole bracket is doubled, so the doubling is the last step done. Undo it first: divide both sides by 2, so x + 3 = 7.
Then undo the + 3: x = 7 − 3 = 4. (Check: 2 × (4 + 3) = 14 ✓.)
A common mistake, and the fix
Dividing only part of a side.
In 2x + 3 = 11, halving the 2x but not the 3 gives x + 3 = 5.5 and the wrong answer 2.5. Undo the + 3 first (2x = 8), then divide both sides by 2 (x = 4), and check: 2 × 4 + 3 = 11.
Try a few
3x − 1 = 14
add 1 to both sides: 3x = 15; divide by 3.
5x + 2 = 17
subtract 2: 5x = 15; divide by 5.
x/2 + 4 = 10
subtract 4: x/2 = 6; multiply by 2.
3(x − 2) = 12
divide by 3 first: x − 2 = 4; then add 2.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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