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Chapter 9 · Questions · page 66 of 68

How do you solve an inequality?

Short answerUse the same steps as an equation, keeping the inequality sign as it is, unless you multiply or divide by a negative. Then flip it. 3x - 4 < 11 becomes x < 5.

levelAlgebra 1
standard7.EE.B.4b
practiceInequalities

An inequality has a whole range of answers instead of one. x < 5 means every number below 5 works. You find the boundary with ordinary equation moves and keep track of which way the sign points.

How to use it

  1. Undo addition or subtraction on both sides.
  2. Divide by the coefficient. If it is negative, flip the sign.
  3. Write the answer with the variable first.
  4. Test one number from your range in the original.

Example

3x−4<11⇒3x<15⇒x<53x - 4 < 11 \Rightarrow 3x < 15 \Rightarrow x < 5
x+6≥2⇒x≥−4x + 6 \ge 2 \Rightarrow x \ge -4

Where it goes wrong

  • Writing x = 5 when the question had an inequality.
  • Flipping the sign after subtracting. Only a negative multiplier or divisor flips it.

Related

Solving an inequalityDividing by a negative flips the sign
Practice this