1. Multi-step Inequalities
Indicator 11
Multi-step Inequalities

2. Example 1: What are the solutions to the inequalities?
a. -6a – 7 ≤17 b. -4 < 5 – 3n c. 50 > 0.8x + 30

3. Example 2:
What are the solutions of 15 ≤ 5 – 2(4m + 7)? Graph the solution.

4. Example 3:
What are the solutions of 3b + 12 > 27 – 2b? Graph the solution.

5. Example 4:
What are the solutions to each inequality? a n ≤ 5n – 1 b x ≥ 7x x

6. Definition
Compound Inequality: 2 distinct inequalities joined by the words and or the word or.
And contains the overlap
of the 2 graphs.
x > 3
x < 7
x > 3 and
Or contains each graph
of the 2 inequalities.
x < -2
x > 1
x < -2 or

7. Definition: Interval Notation
Interval Notation describes the portion of the number line in the answer. 3 different symbols are used in interval notation. Parentheses: Use ( or ) when a < or > symbol indicates the endpoints are not included. Brackets: Use [ or ] when a ≤ or ≥ symbols indicates the endpoints are included. Infinity: Use  when the interval continues forever in a positive direction. Use - when the interval continues forever in the negative direction.

8. Example 5:
What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ - 5? Graph the solution and write the solution using interval notation.

9. Example 6:
What are the solutions of -2 < 3y – 4 < 14? Graph the solution and write it in interval notation.

10. Example 7:
What is the graph of (-2, 7]? How do you write (-2, 7] as an inequality?
b. What is the graph of y > 7? How do you write y > 7 in interval notation?