1.5 Solving Inequalities

Solving and Graphing an Inequality• What is the solution of -3(2x – 5) + 1 ≥ 4? Graph

the solution.

-3(2x – 5) + 1 ≥ 4

-6x + 15 + 1 ≥ 4

-6x + 16 ≥ 4

-6x ≥ -12

x ≤ 2

Using an Inequality• 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?

• Let n = the number of movie rentals in one month.

• First plan: 36 second plan: 15 + 1.5n

36 < 15 + 1.5n

21 < 1.5n

14 < n

• You must rent more than 14 movies in a month for the first plan to cost less.

No Solution or All Real Numbers as Solutions

• Is the inequality always, sometimes, or never true?

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

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

-6x – 2 > -6x + 7

-2 > 7 NEVER TRUE

Since the inequality is false, there is no solution.

No Solution or All Real Numbers as Solutions

• Is the inequality always, sometimes, or never true?

B. 5(2x – 3) – 7x ≤ 3x + 8

5(2x – 3) – 7x ≤ 3x + 8

10x – 15 – 7x ≤ 3x + 8

3x – 15 ≤ 3x + 8

-15 ≤ 8 ALWAYS TRUE

Since the inequality is true, all real numbers are solutions.

Compound Inequality

• 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.

Solving an And Inequality• What is the solution of 7 < 2x + 1 and 3x ≤ 18?

Graph the solution.

7 < 2x + 1 and 3x ≤ 18

3 < x and x ≤ 6

3 < x ≤ 6

Solving an Or Inequality• What is the solution of 7 + k ≥ 6 or 8 + k < 3?

Graph the solution.

7 + k ≥ 6 or 8 + k < 3

k ≥ -1 or k < -5

k < -5 or k ≥ -1

More Practice!!!!!

• Homework – Textbook p. 38 #10 – 43.