SOL 8.15 cont.

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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.

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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