Q. \(123(8x+24)=9-3(x-4)\)

We need to solve the equation:

\[
123(8x+24)=9-3(x-4)
\]

Step 1: Distribute on the left side.

The left side is \(123(8x+24)\). Multiply \(123\) by each term inside the parentheses.

\[
123(8x+24)=123\cdot 8x + 123\cdot 24
\]

Compute each product:

\(123\cdot 8=984\), so \(123\cdot 8x=984x\).

\(123\cdot 24\): note \(123\cdot 24=123\cdot (20+4)=123\cdot 20+123\cdot 4=2460+492=2952\).

So the left side becomes:

\[
123(8x+24)=984x+2952
\]

Now rewrite the equation with this simplified left side.

\[
984x+2952 = 9 – 3(x-4)
\]

Step 2: Distribute on the right side.

The right side is \(9 – 3(x-4)\). First distribute \(-3\) across \((x-4)\).

\[
-3(x-4)=-3x + 12
\]

So the right side becomes:

\[
9 – 3(x-4) = 9 + (-3x + 12) = -3x + 21
\]

Now the equation is:

\[
984x+2952 = -3x+21
\]

Step 3: Get all \(x\)-terms on one side.

Add \(3x\) to both sides to eliminate \(-3x\) on the right.

\[
984x+2952 + 3x = 21
\]

Combine like terms: \(984x+3x=987x\).

\[
987x+2952 = 21
\]

Step 4: Get constants on the other side.

Subtract \(2952\) from both sides.

\[
987x+2952 – 2952 = 21 – 2952
\]

Left side simplifies to \(987x\).

Compute the right side:

\(21-2952 = -2931\).

\[
987x = -2931
\]

Step 5: Solve for \(x\).

Divide both sides by \(987\).

\[
x = \frac{-2931}{987}
\]

Simplify the fraction by noting \(2931=3\cdot 977\) and \(987=3\cdot 329\), but easiest is to check division:

\(987\cdot 3 = 2961\) (too high), so try sign and exact division.

Compute directly:

\(-2931 \div 987 = -3\).

\[
x=-3
\]

Final Answer:

\[
x=-3
\]