Question

How do I do this? What is the answer?

Solve for x: -3|2x + 6| = -12

1)x = 1 and x = 5
2)x = -1 and x = -5
3)x = -9 and x = 3
4)No solution

Answer 1

First, distribute:\[-3\left| 2x+6 \right|=-12\]\[6x+18=-12\]\[6x+(18-18)=(-12)-18\]\[6x=-30\]\[\frac{ 6x }{ 6 }=\frac{ -30 }{ 6 }\]\[x=-5\]I would go for B.

Answer 2

You get it, right?

Answer 3

are you sure? I need to get this question right. And yes I get it but I just want to make sure that the answer is b.

Answer 4

@Michele_Laino

Answer 5

?

Answer 6

is it right?

Answer 7

We can rewrite your equation as follows:
\[\left| {2x + 6} \right| = 4\]
I have divided both sides by -3

Answer 8

now we have to consider these 2 cases:
\[\Large \left\{ \begin{gathered}
2x + 6 \geqslant 0 \hfill \\
2x + 6 = 4 \hfill \\
\end{gathered} \right.\; \cup \,\left\{ {\begin{array}{*{20}{c}}
{2x + 6 < 0} \\
{ - \left( {2x + 6} \right) = 4}
\end{array}} \right.\]

Answer 9

the solutions of your equations are given by the solutions of those system of inequality above

Answer 10

equation*

Answer 11

for example I solve the first system:
I get this:
\[\Large \left\{ \begin{gathered}
2x + 6 \geqslant 0 \hfill \\
2x + 6 = 4 \hfill \\
\end{gathered} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}
{x \geqslant - 3} \\
{x = - 1}
\end{array}} \right.\]
am I right?

Answer 12

since x=-1, belongs to the interval (-3, +infinity), then x=-1 is a solution of your original equation

Answer 13

now, please do the same with the second system:
\[\Large \left\{ {\begin{array}{*{20}{c}}
{2x + 6 < 0} \\
{ - \left( {2x + 6} \right) = 4}
\end{array}} \right.\]