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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Cumulative Assessment

Exercise 9 Page 161

Solve the inequality and choose only integers from the interval.

B

Practice makes perfect

To solve this inequality, let's begin by isolating the absolute value. Since the absolute value is multiplied by 2, we have to divide both sides of the inequality by 2. 2|x-5|<16 ⇔ |x-5|<8 When we remove the absolute value, we get a compound inequality. - 8< x-5<8

If we pull the inequality apart, we need to consider two possible cases. Case 1:& x-5>- 8 Case 2:& x-5< 8 We can solve each inequality separately.

Case 1

x-5>- 8

LHS+5>RHS+5

x>-3

Case 2

x-5<8

LHS+5

x<13

Solution Set

Combing the found inequalities, we get a compound inequality. -3integers. From the interval above, let's separate the integers of the solution set. {-2, -1, 0, 1, 2, ..., 12} Let's add these integers together. (-2)+(-1)+...+12=75 Therefore, the correct answer is B.

Subchapter links

Exercises p.160-161