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# SOL 8.15 cont. PowerPoint PPT Presentation

SOL 8.15 cont. Two-step Inequalities. What is an inequality?. An inequality is a mathematical sentence that compares expressions using: < less than > greater than ≤ less than or equal to ≥ greater than or equal to. Example 1: x/3 – 4 > 8. First, add 4 to both sides.

SOL 8.15 cont.

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## SOL 8.15 cont.

Two-step Inequalities

### What is an inequality?

• An inequality is a mathematical sentence that compares expressions using:

• < less than

• > greater than

• ≤ less than or equal to

• ≥ greater than or equal to

### Example 1: x/3 – 4 > 8

• First, add 4 to both sides.

• Multiply by 3 on both sides.

• x/3 > 12

• x > 36 so any number greater than 36 is a possible solution to this inequality

### !!!!! Special rule !!!!!

• When you multiply or divide by a negative number, the inequality sign reverses. (< becomes > and ≤ becomes ≥)

### Example 2: -2x + 4 ≤ 12

• Subtract 4 from both sides.

• Divide by -2 on both sides

• -2x ≤ 8

• x ≥ -4 the sign flips bc we divided by a negative number

### Example 3: x/-6 – 8 > 3

• Add 8 to both sides

• Multiply by -6 on both sides

• x/-6 > 11

• x < -66 the sign flips bc we multiplied by a negative number

### Graphing Inequalities

• If you have >, you place an “open” (unshaded) circle on the number and shade to the right, including the arrow.

• If you have <, you place an “open” (unshaded) circle on the number and shade to the left, including the arrow.

• If you have ≥, you place a “closed” (shaded) circle on the number and shade to the right, including the arrow.

• If you have ≤, you place a “closed” (shaded) circle on the number and shade to the left, including the arrow.

### Graph the following

• x < -9

• y ≥ 17

• w ≤ -36

• b > 4

Solve the following inequalities, and then graph.

• n/2 – 4 > -10

• -2x + 4 ≤ 12

• 19 ≥ 5x + 4

• w/-2 + 8 < 16

### Question you might see!

• Which is one value of the set of x that makes the following true? 7x + 3 > 17

• 0

• 1

• 2

• 3

D. 3