1.5 – Solving Inequalities Students will be able to:

•Solve and graph inequalities •Write and solve compound inequalities

Lesson Vocabulary•Compound inequality

1.5 – Solving Inequalities Words like “at most” or “at least” suggest a

relationship in which two quantities may not be equal. You can represent such a relationship

with a mathematical inequality.

1.5 – Solving Inequalities

In the graphs above, the point at 4 is a boundary point because it separates the graph

of the inequality from the rest of the number line. An open dot at 4 means that 4 is not a solution. A closed dot at 4 means that 4 is a

solution

1.5 – Solving Inequalities Problem 1:

What inequality represents the sentence “5 fewer than a number is at least 12.”

What inequality represents the sentence, “The quotient of a number and 3 is no more than 15.”

1.5 – Solving Inequalities Problem 2:

What is the solution of -3(2x – 5) + 1 > 4?

Graph your solution.

What is the solution of -2(x + 9) + 5 > 3

Graph your solution.

1.5 – Solving Inequalities Problem 3:

A movie rental company offers two subscription plans. You can pay $36 a month and rent as many movies as desired, or you can pay $15 a

month and $1.50 to rent each movie. How many movies must you rent in a month for the first plan to cost less than the second plan?

1.5 – Solving Inequalities Problem 3b:

A digital music service offers two subscription plans. The first has a $9 membership fee and charges $1 per download. The second has a

$25 membership fee and charges $.50 per download. How many songs must you

download for the second plan to cost less than the first plan?

1.5 – Solving Inequalities Problem 4:

Is the inequality always, sometimes, or never true?

a. -2(3x + 1) > -6x + 7

b. 5(2x – 3) – 7x< 3x + 8

NEVER

ALWAYS

1.5 – Solving Inequalities You can join two inequalities with the word and

or the word or to form a compound inequality.

To solve a compound inequality containing and, find all values of the variable that make both

inequalities true.

To solve a compound inequality containing or, find all values of the variable that make AT

LEAST ONE of the inequalities true.

1.5 – Solving Inequalities Problem 5:

What is the solution of 7 < 2x + 1 and 3x < 18? Graph the solution.

b. What is the solution of 5 < 3x – 1 and 2x < 12? Graph the solution

3 < x and x < 6

x > 2 and x < 6

1.5 – Solving Inequalities You can collapse a compound and inequality,

like 5 < x + 1 and x+ 1 < 13, into a simpler form, 5 < x + 1 < 13.

Problem 5b:Solve -6 < 2x – 4 < 12. Graph the solution.

-1 < x < 8

1.5 – Solving Inequalities Problem 6:

What is the solution of 7 + k > 6 or 8 + k < 3? Graph the solution.

b. What is the solution of 3x > 3 or 9x < 54? Graph the solution

k > -1 or k < -5

All real numbers