Solve the proportion for x in the equation (x - 5)/8 = 3/4. What is x?

To solve the proportion ((x - 5)/8 = 3/4), we begin by cross-multiplying. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other, establishing the equality between the two products:

[

(x - 5) \cdot 4 = 3 \cdot 8

]

This simplifies to:

[

4(x - 5) = 24

]

Next, we distribute the 4 on the left side:

[

4x - 20 = 24

]

To isolate (4x), we add 20 to both sides:

[

4x = 24 + 20

]

This simplifies to:

[

4x = 44

]

Now, we divide both sides by 4 to solve for (x):

[

x = \frac{44}{4} = 11

]

Thus, the value of (x) is 11. This solution is confirmed by substituting (x) back into the original equation and ensuring both sides are equal, which validates that the solution is indeed correct. Therefore, the correct answer is that (x =