Question

[02.03]

Solve for x: −5|x + 1| = 10 (1 point)

x = 0
x = −3 and x = 1
x = −1 and x = 3
No solution

Answer 1

to deal with absolute value first get rid of any number which is outside absolute value \[\left| \right|\]
so first divide both sides by-5
what would you get on left and right side ??

Answer 2

I thought that I would add 5 to both sides?

Answer 3

good point!
\[-5\left| x+1 \right|=10\] is same as \[-5 * \left| x+1 \right|=10\]
there is multiplication..therefore we should do opposite of multiply to get rid of -5

Answer 4

if it was \[-5 + \left| x+1 \right|=10\]
then you would add 5 both sides

Answer 5

Oh, I for what the | lines mean

Answer 6

|x + 1|= 2?

Answer 7

yeah thats the absolute value sign
for example \[\left| x \right| \] the absolute value of x

Answer 8

what is 10 divide by -5 = ??

Answer 9

-2

Answer 10

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

Answer 11

wait waaa

Answer 12

i thought that was just to get rid of the -5

Answer 13

correct the absolute value of a number would always be positive
there is some rule to solve absolute value \[ \left| x \right| = k\]
where `k` is constant which should be positive \[k \ge 0\]

Answer 14

Wait, Im confused.

Answer 15

`i thought that was just to get rid of the -5`
right so -5/-5 is just one \[\frac{ \cancel{-5 }\left| x+1 \right| }{\cancel{ -5} } = \frac{10}{-5}\] \[\left| x+1 \right|=-2\]
i was just trying to write each step ..

Answer 16

here is an example \[\left| x \right| =- k\] where k is constant
then the equation has no solution

Answer 17

\[\left| a+5 \right| = -9 ~~~ ~~~~~~~\left| x^2+8 \right|=-5\]
more e xamples
the equations doesn't have any solution
you can't solve from there because there is a negative side to the opposite side of the absolute value

Answer 18

\[ \rm \left| x \right| = k \]
(k is constant) in order to find the solution that k must be positive
otherwise no solution

Answer 19

after you divide both sides by -5, you get
| x+1|= -2

the left side | x+1 | means "whatever x+1 is, make it positive"
for example, if x was -2: | -2 + 1 | becomes | -1| and the | | means make the -1 a +1
so |-2+1| becomes (is the same as) 1

however, notice this: no matter what x we put inside | x+1 |
the | | will make the answer positive.
in other words, there is no way to make |x+1| equal a -2
so there is no solution i.e. no x that makes this equation true.