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HW #14 Solutions: Handout 1) x > 0 and x < 3 -Infinite solutions, all real #s between 0 and 3. -There is no absolute largest or smallest value. -0 and 3 2) x < 1 or x ≥ 3 3) x < 2 or x > 2, can be written as x≠2 4) x = 4 and x = 4 5) 6) 7) x = 4 or x = 3 5 4 2 3 1 1 0 2 3 5 4 8) 5 4 3 2 1 0 1 2 3 4 5 9) x < 2 or x = 2 5 4 3 2 1 0 1 2 3 4 5 1) The addition property of equality is being applied since 9 is being added to both sides of the equation. 6 3 9 2) -27x y z 4) Sometimes true 3) S = ±√1- A C Aim #15: How do we solve compound inequalities? HW: Handout 2 Do Now: a. Solve w = 121, for w. Graph the solutionon a number line. 0 2 b. Solve w < 121, for w. Graph the solution on a number line and write the solution set as a compound inequality. 0 2 c. Solve w ≥ 121, for w. Graph the solution on a number line and write the solution set as a compound inequality. 0 Consider the compound inequality-5 < 2x + 1 < 4 a. Rewrite the inequality as a compound statement of inequality. b. Solve each inequality for x. Then, write the solution to the compound inequality. c. Graph the solution set on the number line below. Describe all possible values of x. 0 d. Let's solve -5 < 2x + 1 < 4 without rewriting it and write the solution in two different ways. -5 < 2x + 1 < 4 Given x + 4 < 6 or x - 1 > 3 a. Solve each inequality for x. Then, write the solution to thecompound inequality. x + 4 < 6 or x - 1 > 3 b. Graph the solution set on the number line below and describe all possible values of x. 0 Solve each compound inequality for x and graph the solutionon a number line. a. x + 6 < 8 and x - 1 > -1 b. 6 ≤ x ≤ 11 2 c. 5x + 1 < 0 or 8 ≤ x-5 d. 10 > 3x - 2 or x = 4 e. x - 2 < 4 or x - 2 > 4 f. x - 2 ≤ 4 and x - 2 ≥ 4 g. 1 + x > -4 or 3x - 6 > -12 h. 1 + x > -4 or 3x - 6 < -12 i. 1 + x > 4 and 3x - 6 < -12 j. 7 ≤ -2x + 21 < 31 k. -3 < j+2 <7 2 LET'S SUM IT UP! "or" The solution to a compound inequality separated by ________ should be aunion of either numbers included in ____________of the two solution sets. "and" The solution to a compound inequality separated by __________ is only thevalues both that are in ___________ of the individual solution sets. This should be the intersection ___________________of the two solution sets. If a compound inequality is separated by "or" it is possible for the solution set to be all real numbers. However it is not possible to have no solution. If a compound inequality is separated by "and" it is possible to have no solution. However it is not possible for the solution to be all real numbers.