Question

For this item, enter the answer in the space provided.

Consider the equation.

5 ( x - 8) + 7 = 4 (x - 6) - 9
What is the value of
in the equation?

Answer 1

Are you sure?

Answer 2

To solve the equation \(5 (x - 8) + 7 = 4 (x - 6) - 9\), we will first simplify both sides.

1. Distribute the 5 on the left side:
\[
5x - 40 + 7 = 4(x - 6) - 9
\]

This simplifies to:
\[
5x - 33 = 4(x - 6) - 9
\]

2. Now, we distribute the 4 on the right side:
\[
5x - 33 = 4x - 24 - 9
\]

This simplifies to:
\[
5x - 33 = 4x - 33
\]

3. Next, we can subtract \(4x\) from both sides:
\[
5x - 4x - 33 = -33
\]
Which simplifies to:
\[
x - 33 = -33
\]

4. Now add 33 to both sides:
\[
x = 0
\]

Thus, the value of \(x\) in the equation is \(0\).

Answer 3

Let's double-check the calculations step by step to ensure everything is correct.

We start with the equation:

\[
5 (x - 8) + 7 = 4 (x - 6) - 9
\]

**Step 1: Distribute on both sides.**

On the left:

\[
5(x - 8) + 7 \implies 5x - 40 + 7 = 5x - 33
\]

On the right:

\[
4(x - 6) - 9 \implies 4x - 24 - 9 = 4x - 33
\]

So the equation simplifies to:

\[
5x - 33 = 4x - 33
\]

**Step 2: Isolate \(x\).**

Subtract \(4x\) from both sides:

\[
5x - 4x - 33 = -33
\]

This simplifies to:

\[
x - 33 = -33
\]

Now, add \(33\) to both sides:

\[
x = 0
\]

The calculations confirm that the value of \(x\) is indeed \(0\).

If you have a specific aspect of the solution you'd like to discuss or question further, please feel free to ask!