1.4 - Solving Inequalities

Solving Inequalities

Same rules as solving equations

• Distribute

• CLT

• Get variables on the same side

• Add/subtract constants

• Multiply/divide coefficients​

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When you multiply or divide both sides by a negative, you FLIP the inequality sign!

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​SPECIAL RULE

​​Flip?

Flip?

Multiple Choice

Decide if the following inequality will need to be flipped:

$$x-3<-16$$  

• Flip!

• Do not flip!

Multiple Choice

Decide if the inequality will need to be flipped:

$$-6x+5\ge35$$  

• Flip!

• Do not flip!

Multiple Choice

Decide if the following inequality will need to be flipped:

$$\frac{x}{2}+4>-7$$  

• Flip!

• Do not flip!

Closed Cirlce!

​

Open Circle!​

​Graphing Inequalities

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Direction of the arrow

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Multiple Choice

Open dot or closed dot?

$$g<-14$$  

• Open dot

• Closed dot

Multiple Choice

Open dot or closed dot?

$$y\ge5$$  

• Open dot

• Closed dot

Multiple Choice

Which way will the arrow on the number line point?

$$x<-6$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$h\ge8$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$-3<f$$  

• Left

• Right

Draw

Graph the inequality on the number line:

$$x<-4$$  

Multiple Choice

Solve the following inequality:

$$2x-5<13$$  

• x < 4

• x < 9

• x > 9

• x > 4

Multiple Choice

Solve the following inequality:

$$-3x-5\le22$$  

• $$x\le-9$$  

• $$x\ge-9$$  

• $$x\le\frac{-17}{3}$$  

• $$x\ge\frac{-17}{3}$$  

Multiple Choice

Solve for x. (Use the image to identify the correct inequality and graph.)

$$x\ -\ 1\ \le\ -9$$  

• A

• B

• C

• D

Multiple Choice

Solve for x. (Use the image to identify the correct inequality and graph.)

$$\frac{x}{8}\ >\ 4$$  

• A

• B

• C

• D