Lesson 5.5: Solve Inequalities with Multiplication and Division

Lesson 5.5

Solve Inequalities using Multiplication and Division

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Definition:

Multiplication and Division Properties of Inequality: when we divide or multiply by a negative number across and inequality, we have to flip the sign of the inequality.

Subject | Subject

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​Key Concept:

​Solving Inequalities with multiplication or division is the exact same as solving equations by multiplication or division. The one Key Thing to remember is, when you multiply or divide by a negative number, you MUST flip the sign of the inequality!

Multiple Choice

$$\frac{1}{4}x\ +\ 5\ \ge10$$

• $$x\le10$$

• $$x\ge20$$

• $$x\ \le\frac{5}{4}$$

• $$x\ge\frac{5}{4}$$

​Solve: -3x - 4 < 8

Multiple Choice

Solve -4x - 5 > 15

• x < 5

• x > 5

• x < -5

• x > -5

Multiple Choice

Solve: $$-\frac{1}{3}x\ +\ 5\ \ge6$$

• $$x\ \ge3$$

• $$x\ \le3$$

• $$x\ge-3$$

• $$x\le-3$$

​Conclusion: Write two complete sentences about what you learned.