Answered

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What is the solution for [tex]\( x \)[/tex] in the equation?

[tex]\[
\frac{5}{3} x + 4 = \frac{2}{3} x
\][/tex]

A. [tex]\( x = -\frac{12}{7} \)[/tex]

B. [tex]\( x = \frac{12}{7} \)[/tex]

C. [tex]\( x = 4 \)[/tex]

D. [tex]\( x = -4 \)[/tex]

Sagot :

GinnyAnswer
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]
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