Sure, let's solve the equation step-by-step:
Given the equation:
[tex]\[
\frac{3x}{5x + 2} = -4
\][/tex]
### Step 1: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by the denominator [tex]\( (5x + 2) \)[/tex]:
[tex]\[
3x = -4(5x + 2)
\][/tex]
### Step 2: Distribute the right-hand side
Distribute [tex]\(-4\)[/tex] across [tex]\( (5x + 2) \)[/tex]:
[tex]\[
3x = -4 \cdot 5x - 4 \cdot 2
\][/tex]
[tex]\[
3x = -20x - 8
\][/tex]
### Step 3: Move all terms involving [tex]\( x \)[/tex] to one side
Add [tex]\( 20x \)[/tex] to both sides to get all [tex]\( x \)[/tex]-terms on one side:
[tex]\[
3x + 20x = -8
\][/tex]
[tex]\[
23x = -8
\][/tex]
### Step 4: Solve for [tex]\( x \)[/tex]
Divide both sides by 23:
[tex]\[
x = \frac{-8}{23}
\][/tex]
So, the solution to the equation [tex]\(\frac{3x}{5x + 2} = -4\)[/tex] is:
[tex]\[
x = -\frac{8}{23}
\][/tex]
