Question

Solve for x: -3|x - 3| = -6

x = 1, x = -1
x = 1, x = 5
x = 0, x = 5
No solutions

Answer 1

any one?

Answer 2

First things first, you need to get the absolute value by itself, So lets divide both sides by -3

\[\large |x-3| = 2\]

Now this breaks into 2 equations

\(\large x - 3 = 2\) and \(\large x - 3 = -2\)

Solve those 2 equations for 'x'

Answer 3

im still confused

Answer 4

On what? :)

Answer 5

So we start with

\[\large -3|x - 3| = -6\]

The first goal here, is to get the absolute value by itself...and we see it is being multiplied by a -3...so we need to divide both side of the equation by -3 to cancel that out

\[\large \frac{-3|x - 3| = -6}{-3} = \frac{\cancel{-3}|x - 3| = \cancel{-6}\rightarrow 2 }{\cancel{-3}} \]

which leaves us with \[\large |x- 3| = 2\]

Now we know that absolute values change negative numbers into positive...so in a way to show this...we break the equation we have now, into 2 equations...because if we look at that equation we have now...we can either get 2....or 02...and they will both be correct since the 2 would be changed to a 2

First equation:
\[\large x - 3 = 2\]

Second equation:
\[\large x - 3 = -2\]

And solve for 'x' in both cases

Answer 6

so would be B.) ?

Answer 7

Correct indeed :)

Answer 8

thank you so much.

Answer 9

Anytime!