Question

I HAVE TO TURN THIS IN IN 2 HOURS!!! PLEASE HELP!! I have the graph "y=(1/2)|x-3|-2" graphed but the question also wants the solutions. What solution is it referring to?

(I have another graph with the equation of "3|x+4|-5=-2" (again it is graphed already but it also wants the solutions) and the equation "(2/3)|x+4|+3=2" (graphed but I need the solutions))

I don't know what it means by solutions. An explanation and a solved example would be appreciated

Answer 1

1. Solutions for y=(1/2)|x-3|-2: x = -1 or x = 7

2. Solutions for 3|x+4|-5=-2: x= -5 or x =-3

3. Solutions for (2/3)|x+4|+3=2: No solution

Explanation:

Solving for 1. You have to isolate the absolute value

y = (1/2)|x-3|-2

Let y = 0

0 = (1/2)|x-3|-2

Add 2 to both sides

2 = (1/2)|x-3|

Multiple by 2 to both sides

4 = |x-3|

When you have an absolute value, the, whatever the absolute value equals to can be either positive or negative. In this case -4 or +4. Solve for both:

-4 = x-3

x= -1

4 = x-3

x = 7

If you want me to explain 2, let me know.

There is no solution for 3. because you end up getting just a negative number and when you have absolute value, you can't have a negative.