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]
