6 5 Solving Open Sentences Absolute Value is

6. 5 Solving Open Sentences

Absolute Value is a term that refers to a number’s ‘distance from 0’. Because distance is always positive, the answer to an absolute value problem is always positive. - 5 5 The absolute value of – 5 is 5 and the absolute value of 5 is 5 because both numbers are 5 spaces away from 0 on a number line. So what’s inside an absolute value symbol could be positive or negative, but the answer would always be positive! -6 6 Remember that the answer is written below the problem

a- 4 = 3 What is inside the absolute value symbol can be positive or negative. That means there are two problems to do! Then solve each! a– 4=3 and a=3+4 a=7 There are two answers here, 7 and 1. Both, when used in place of ‘a’ will result in 3 for an absolute value answer! - ( a – 4) = 3 -a+4=3 -a=3– 4 -a = - 1 a=1 Notice that I copied the portion of the problem that was inside the absolute value symbols exactly for one problem. Then, I copied it again for the second problem, BUT PLACED A NEGATIVE SIGN OUTSIDE THE PARENTHESES because I need to solve for the negative part of the problem too!

t + 5 9 This problem is solved exactly the same way! t+5 9 t 9– 5 t 4 - (t + 5) 9 - t -5 9 -t 9+5 - t 14 t ˃ - 14 Don’t forget to flip the inequality sign when you change the sign on the ‘t’!

2 x + 8 6 You already know how to solve these problems! Don’t forget to flip the sign! Graphing is the same for inequalities! -7 -1