Absolute Values

Question 1

How many expression do you split this into?

| x + 2 | = 3

Answer 1

two

x + 2 = 3 and x + 2 = -3

Question 2

what is a key step in solving this equation?

2 + | z - 5 | = 10

Answer 2

you have to subtract the two first!

so you get:

then, z - 5 = 8 and z - 5 = -8

z - 5 | = 8

Question 3

what are the two expression to solve from the question | x | < 3 ?

Answer 3

first the positive one is
x < 3

for the negative one you flip the inequality and change to negative so, x > -3

Question 4

solve | x + 5 | > 12

Answer 4

first, x + 5 > 12 and simplify to get x > 7

second, x + 5 < -12 and simplify to get x < -17