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SOL 8.15 cont.

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.

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  1. SOL 8.15 cont. Two-step Inequalities

  2. 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

  3. 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

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

  5. 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

  6. 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

  7. 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.

  8. Graph the following • x < -9 • y ≥ 17 • w ≤ -36 • b > 4

  9. Your turn! Solve the following inequalities, and then graph. • n/2 – 4 > -10 • -2x + 4 ≤ 12 • 19 ≥ 5x + 4 • w/-2 + 8 < 16

  10. 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

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