Solve for an Unknown Number of Changes
Use inverse operations to solve a signed two-step equation.
Supplied materials
- Paper or a note app.
- Fictional position starts at −8 units and rises 3 units each interval. Its final position is 7 units. Let x count intervals.
Learn the idea
The start and repeated change make an equation: −8 + 3x = 7. Here x is an unknown count of equal intervals. First remove the starting offset by adding eight to both sides; the repeated changes must total fifteen units.
Divide both sides by the rate three to find the interval count. Applying the same operation to both sides preserves equality. Substitute the result into the original equation to check the entire story, not only the final division.
- Write −8 + 3x = 7 and label x as the interval count.
- Add eight to each side, giving 3x = 15.
- Divide by three, then substitute x = 5 to check the final position.
See the method in action
−8 + 3x = 7 leads to 3x = 15 and x = 5. Checking −8 + 3 × 5 = −8 + 15 = 7 confirms five intervals.
Check your reasoning
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See the answer and explanation
4
Add seven to get 4x = 16, then divide by four: x = 4. The check is −7 + 4 × 4 = 9.
Take it further
Change the final position to 13: −7 + 4x = 13. Then 4x = 20 and x = 5, one more interval than before.
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