MOSTMATHHome

Chapter 9 · Questions · page 67 of 68

When do you flip the inequality sign?

Short answerOnly when you multiply or divide both sides by a negative number. Adding and subtracting never flip it, even with negative numbers.

levelAlgebra 1
standard7.EE.B.4b
practiceInequalities

Multiplying by a negative reverses the order of numbers: 2 is less than 5, but -2 is greater than -5. The sign flips to keep the statement true. Adding or subtracting slides everything the same way, so the order stays.

How to use it

  1. Watch the step where you divide by the coefficient.
  2. Negative coefficient: flip the sign in that same step.
  3. Or avoid it: move the variable term to the side where its coefficient is positive.

Example

−4x+1≥13⇒−4x≥12⇒x≤−3-4x + 1 \ge 13 \Rightarrow -4x \ge 12 \Rightarrow x \le -3
−2x>8⇒x<−4-2x > 8 \Rightarrow x < -4

Where it goes wrong

  • Flipping when subtracting a negative number.
  • Forgetting to flip, then getting a range where every test number fails.

Related

Dividing by a negative flips the signSolving an inequalityWhen the x term is negative
Practice this