Question

Solve for x: −5|x + 1| = 10

Answer 1

x = 0

x = −3 and x = 1

x = −1 and x = 3

No solution

Answer 2

@tanya123

Answer 3

@hba @jim_thompson5910

Answer 4

First you must isolate the absolute value. So divide both sides by -5 to get


\[\Large -5|x+1| = 10\]

\[\Large \frac{-5|x+1|}{-5} = \frac{10}{-5}\]

\[\Large \frac{\cancel{-5}|x+1|}{\cancel{-5}} = \frac{10}{-5}\]

\[\Large |x+1| = -2\]


What do you notice about the last equation?

Answer 5

The absolute value is by itself?

Answer 6

what else

Answer 7

I don't know

Answer 8

what does absolute value represent in general?

Answer 9

The value of a number without signs or anything

Answer 10

it also represents distance

for example |-7| = 7 and this says "the number -7 is seven units away from 0"

Answer 11

since negative distance makes no sense, it means that the result of an absolute value expression is never negative

Answer 12

Saying

\[\Large |x+1| = -2\]

makes no sense. So therefore, there are no solutions to that equation.

Answer 13

There is no way to make the left side of

\[\Large |x+1| = -2\]

equal to -2 (or any negative number for that matter) regardless of any x value you pick.

Answer 14

So if the answer is a negative number, there is no solution?

Answer 15

if you have something of the form |x| = -2 or |x| = -7, then it's not possible so there are no solutions

Answer 16

Thank you!

Answer 17

np