Q. \(24 – 11 \cdot 5x = 59\)

Let’s first rewrite the problem in a clear mathematical way.

The given equation is:

\[
24 – \frac{11}{5}x = 59
\]

We will solve for \(x\) step by step.

Step 1: Subtract 24 from both sides.

Start with:

\[
24 – \frac{11}{5}x = 59
\]

Subtract \(24\) from both sides so that the \(24\) moves to the other side:

\[
24 – 24 – \frac{11}{5}x = 59 – 24
\]

Simplify:

\[
-\frac{11}{5}x = 35
\]

Step 2: Multiply both sides by \(-\frac{5}{11}\).

We have:

\[
-\frac{11}{5}x = 35
\]

To solve for \(x\), multiply both sides by the reciprocal of \(-\frac{11}{5}\), which is \(-\frac{5}{11}\):

\[
\left(-\frac{5}{11}\right)\left(-\frac{11}{5}x\right) = 35\left(-\frac{5}{11}\right)
\]

On the left, the fractions cancel:

\[
x = 35\left(-\frac{5}{11}\right)
\]

Step 3: Compute the right-hand side.

Compute:

\[
35\left(-\frac{5}{11}\right) = -\frac{35 \cdot 5}{11}
\]

Simplify \(35 \div 11\). Since \(35 = 11 \cdot 3 + 2\), we can reduce directly by noting:

\[
-\frac{35 \cdot 5}{11} = -5 \cdot \frac{35}{11}
\]

Because \(35/11\) does not reduce to an integer, multiply fully:

\[
-\frac{35 \cdot 5}{11} = -\frac{175}{11}
\]

Final Answer:

\[
x = -\frac{175}{11}
\]