Question

What is the solution set of |2x – 3| – 8 = –1?

Answer 1

you need to understand what the ABSOLUTE VALUE is.

The law for ABSOLUTE VALUE is as follows:

\[|x| = x\] if \[x \ge 0\]

and similarly

\[|x| = -x\] if \[x \lt 0\]

Answer 2

x=5,-2

Answer 3

dont listen to him, its not right

Answer 4

so you have to now set up two seperate cases for which x can be POSITIVE _OR_ x can be NEGATIVE. As in the Absolute value law I showed you above.

Answer 5

following the FIRST law where we are assuming x >= 0 (POSITIVE):

solve for 2x-3-8 = -1
x = 5

Plugin a value less than 5 and more than 5 and see what result you get. Construct a number line and plot your signs or a sign table. Then you would find the INTERVAL in which the numbers within the interval suffice the first law whereby x is positive

following the SECOND law where we are assuming x < 0 (NEGATIVE):

solve for -(2x-3)-8=-1
x = -2

Plugin a value less than -2 and more than and see what result you get. Construct a number line and plot your signs or a sign table. Then you would find the INTERVAL in which the numbers within the interval suffice the first law whereby x is negative.

What I suggest you do is rewrite the initial equation by taking the 8 over and doing the same procedure above.

Im not going to give you the answer, you do it.