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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.

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sol 8 15 cont

SOL 8.15 cont.

Two-step Inequalities

what is an inequality
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
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
!!!!! Special rule !!!!!
  • When you multiply or divide by a negative number, the inequality sign reverses. (< becomes > and ≤ becomes ≥)
example 2 2x 4 12
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
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
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
Graph the following
  • x < -9
  • y ≥ 17
  • w ≤ -36
  • b > 4
your turn
Your turn!

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
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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