1.5 Solving Inequalities.

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Presentation transcript:

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 21 < 1.5n 14 < n 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.