Question

Solve the equation for the values of x.
|4 + 5x| + 3x = 12

Answer 1

X =1

Answer 2

\(\bf |4 + 5x| + 3x = 12\implies |4 + 5x| =12-3x\implies
\begin{cases}
+(4 + 5x) =12-3x\\ \quad \\
\bf -(4 + 5x) =12-3x
\end{cases}\)

Answer 3

hmm

Answer 4

\(\bf |4 + 5x| + 3x = 12\\ \quad \\\implies |4 + 5x| =12-3x\implies
\begin{cases}
+(4 + 5x) =12-3x\\ \quad \\
\bf -(4 + 5x) =12-3x
\end{cases}\)

Answer 5

What? I don't understand any of that...

Answer 6

an absolute value expression, gives 2 results, because it splits into two scenarios, those 2 above

so you solve both and you'd get 2 values for "x"

Answer 7

all we did firstly is, isolate the absolute value expression on the left-hand side

Answer 8

To solve an absolute value equation of the form
\( |X| = b\)
where \(X\) is an expression in x,
split it up into the two equations
\( X = b\) or \(-X = b\)
Then solve the two equations and separate the answers with the word "or."

Answer 9

This is what @jdoe0001 explained above.

You started with
|4 + 5x| + 3x = 12

The first step is to change it to
|4 + 5x| = 12 - 3x by subtracting 3x from both sides.

Now apply the rule above:
4 + 5x = 12 - 3x or -(4 + 5x) = 12 - 3x

This is the result that jdoe001 showed above.

Now you solve both equations and separate the answers with the word "or."

Answer 10

OH! Ok, Thanks for the breakdown @mathstudent55 !!! SOOOO HELPFUL!

Answer 11

You're welcome.