Answered

What is the value of [tex]$x$[/tex] in this proportion?

[tex]\frac{5}{6} = \frac{-4}{x + 2}[/tex]

A. [tex]x = -2 \frac{4}{5}[/tex]
B. [tex]x = -4 \frac{2}{5}[/tex]
C. [tex]x = -5 \frac{1}{5}[/tex]
D. [tex]x = -6 \frac{4}{5}[/tex]



Answer :

To solve the proportion \(\frac{5}{6} = \frac{-4}{x + 2}\) for \(x\), follow these steps:

1. Cross-multiplication:
We start by cross-multiplying to eliminate the fractions:
[tex]\[ 5(x + 2) = -4 \cdot 6 \][/tex]

2. Simplify both sides:
Next, we expand and simplify both sides of the equation:
[tex]\[ 5x + 10 = -24 \][/tex]

3. Isolate the variable \(x\):
To isolate \(x\), subtract 10 from both sides:
[tex]\[ 5x = -24 - 10 \][/tex]
Simplifying the right-hand side:
[tex]\[ 5x = -34 \][/tex]

4. Solve for \(x\):
Finally, divide both sides by 5 to solve for \(x\):
[tex]\[ x = \frac{-34}{5} \][/tex]

Therefore, the value of \(x\) is:
[tex]\[ x = -6.8 \][/tex]

As a mixed number, \(-\frac{34}{5}\) can be converted by recognizing that 34 divided by 5 is 6 with a remainder of 4:
[tex]\[ -\frac{34}{5} = -6 \frac{4}{5} \][/tex]

Thus, the correct answer is:

[tex]\[ x = -6 \frac{4}{5} \][/tex]

So the correct option is:
[tex]\[ x = -6 \frac{4}{5} \][/tex]