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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.

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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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