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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.