Solve for x: −5|x + 1| = 10 (1 point)

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

Question

Solve for x: −5|x + 1| = 10 (1 point)

	x = 0
	x = −3 and x = 1
	x = −1 and x = 3
	No solution

zepdrix · Answer

How bout divide both sides by -5 as a first step?
What equation does that leave you with?

iblue · Answer

x + 1 = -2

zepdrix · Answer

Mmm ok good. We still have to deal with the absolute value though :)
|x+1| = -2

zepdrix · Answer

In general, we can rewrite an absolute value by splitting it into two equations, a positive and a negative.
$\large\rm |x|=\pm x$

zepdrix · Answer

So we'll have two equations,

  (x+1) = -2
and
-(x+1) = -2

zepdrix · Answer

And then solve for x.
You should end up with two solutions,
one from each equation.

zepdrix · Answer

Confused? :O

iblue · Answer

Um, Very much so.

zepdrix · Answer

Ahh I ran off for a minute D: sorry

zepdrix · Answer

We could go a little more in depth about absolute value but I fear that will just make things more complicated.

So just try to remember this much:
Absolute value bars can be dropped and replaced with a plus/minus symbol.
$\large\rm |x|=\pm x$
It corresponds to a positive sometimes,
and a negative at other times.

$\large\rm |x|=~~~x$
and
$\large\rm |x|=-x$

iblue · Answer

Can you give me step by step direction of on how to answer this question. I have like 6 more just like this and I don't want to keep asking the question

zepdrix · Answer

$$\large\rm -5|x+1|=10$$Start by trying to isolate your absolute value stuff.
For this particular problem, notice that -5 is `multiplying` the absolute value.
So we "undo" multiplication with division,$$\large\rm |x+1|=-2$$Now we replace absolute value bars with plus/minus symbol,$$\large\rm \pm(x+1)=-2$$So this is actually two equations, a plus and a minus equation.

When dealing with the plus,
$\large\rm +(x+1)=-2$
we can simply drop the brackets,
$\large\rm x+1=-2$
and solve for x, subtracting 1 from each side,
$\large\rm x=-3$

When dealing with the negative,
$\large\rm -(x+1)=-2$
We'll distribute the negative to each term in the brackets,
no no no, actually let's multiply both sides by -1, that's easier,
$\large\rm x+1=2$
and again, solve for x by subtracting 1 from each side,
$\large\rm x=1$

zepdrix · Answer

So it's a matter of ...
`Step 1: Isolate your absolute value stuff`
`Step 2: Drop absolute value, creating two equations`
`Step 3: Solve for x in each case.`

zepdrix · Answer

Is the splitting sort of a weird confusing step?
Think you can replicate it in your other problems? :)

iblue · Answer

I somewhat get it.

iblue · Answer

My answer choice are complete diff. here they are

zepdrix · Answer

For the first problem, we ended up with
x=-3 and x=1.

That's one of the answer choices, ya? :o

iblue · Answer

Yes

zepdrix · Answer

So ya, this one worked out to answer... B or whatever.
So maybe you should try working out the next one on your own and lemme know if you get stuck. Or if we need to work through one more to make this concept really "click" that would be fine also.

zepdrix · Answer

Either way,
$\large\rm \color{#33B111}{\text{Welcome to OpenStudy! :)}}$

sshayer · Answer

$$\left| x+1 \right|=-2$$
which is impossible 
as$$\left| x+a \right|= positive~quantity.$$

joannablackwelder · Answer

Yeah, I agree with no solution, since a negative quantity times a positive quantity can never be positive.

zepdrix · Answer

AHHHH sorry D:<
I forgot about that...