What you’ll learn
Solve. Enter an exact answer or an equivalent intermediate statement.
Key idea
Add or subtract the same value on both sides, or multiply or divide by a positive value, and the inequality direction stays the same. Multiplying or dividing both sides by a negative reverses the order, so flip the sign.
After solving, describe the full set of values, not one answer. Test a value from the solution set in the original inequality and a value outside it. This helps catch a missed sign reversal.
Worked example
Solve. Enter an exact answer or an equivalent intermediate statement.
(6)x + (5) <= -4
- (6)x <= -9
- x <= -3/2
Answer: x <= -3/2
Quick Check
Analyze the proposed student response. Choose Correct or Incorrect.
(-7)x + (-5) <= 23 Student response: x >= -4