To find the solution for [tex]\( x \)[/tex] in the equation
[tex]\[
\frac{5}{3} x + 4 = \frac{2}{3} x
\][/tex]
let's follow a step-by-step solution.
1. Start by simplifying the equation:
[tex]\[
\frac{5}{3} x + 4 = \frac{2}{3} x
\][/tex]
2. Subtract [tex]\(\frac{2}{3} x\)[/tex] from both sides to get the terms with [tex]\( x \)[/tex] on one side:
[tex]\[
\frac{5}{3} x - \frac{2}{3} x + 4 = 0
\][/tex]
3. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
\left(\frac{5}{3} - \frac{2}{3}\right)x + 4 = 0
\][/tex]
[tex]\[
\frac{3}{3} x + 4 = 0
\][/tex]
[tex]\[
x + 4 = 0
\][/tex]
4. Isolate [tex]\( x \)[/tex] by subtracting 4 from both sides:
[tex]\[
x = -4
\][/tex]
Therefore, the correct answer is:
D. [tex]\( x = -4 \)[/tex]
