What you’ll learn
Given an equation of the form px + q = r or p(x + q) = r with specified rational coefficients and a unique solution, solve fluently by reversing the operation sequence and verify the solution by substitution.
Key idea
In an equation of the form ax + b = c, first undo the addition or subtraction attached to ax. Then divide or multiply to isolate x.
Check a proposed value in the original equation, not only in a rearranged line. Substitution should make the left and right sides equal. If coefficients are negative or fractions, preserve their signs and use exact arithmetic when possible.
Worked example
Solve the two-step equation and check the result.
5x - 3 = 17
- 5x = 20
- x = 4
Answer: 4
Quick Check
Analyze the proposed student response. Choose Correct or Incorrect.
-6x - 12 = -60 Student response: 8