Question

I need help to figure how in the world you can get X=-5 from this equation?

|2x-3|+4=17. The question is: What are the solutions to the equation |2x-3|+4=17? The final answer is: "X=-5 or X=8". But I do not understand how you can get X=-5 from this. Can someone please explain?

Answer 1

bearing in mind that an absolute value expression, is in effect a piece-wise expression, so once we remove the bars, we really end up with two siblings, one is negative, the other positive, of the same expression.

`\bf |2x-3|+4=17\implies |2x-3|=13\implies \begin{cases} +(2x-3)=13\\ 2x-3=13\\ 2x=16\\[1em] x=\cfrac{16}{2}\\[1em] \boxed{x=8}\\[-0.5em] \hrulefill\\ -(2x-3)=13\\ -2x+3=13\\ -2x=10\\[1em] x=\cfrac{10}{-2}\\[1em] \boxed{x=-5} \end{cases}`

Answer 2

x=-5 and x=8

Explanation:

|2x-3|+4=17

first step is to get the absolute value alone

subtract 4 from each side

|2x-3|+4-4=17-4

|2x-3|=13

absolute value equations have 2 solutions, one positive and one negative

now we can separate the equation into positive and negative

2x-3 = +13 and 2x-3 = -13

add 3 to each side

2x-3+3 = 13+3 2x-3 + 3 = -13 +3

2x = 16 2x = -10

divide by 2

2x/2 = 16/2 2x/2 = -10/2

x = 8 x = -5

the two solutions are x = -5 and x = 8

lets check

|2x-3|+4=17

x=-5

|2(-5)-3|+4=17

|-10-3|+4=17

|-13|+4=17

absolute values means positive

13+4 = 17

|2x-3|+4=17

x=8

|2(8)-3|+4=17

|16-3|+4=17

|3|+4=17

absolute values means positive

3+4 = 17