Question

This equation has one solution.

5(x – 1) + 3x = 7(x + 1)

What is the solution?

Answer 1

To solve the equation \( 5(x – 1) + 3x = 7(x + 1) \), let's start by expanding both sides.

1. Expand the left side:
\[
5(x - 1) = 5x - 5
\]
So,
\[
5(x - 1) + 3x = 5x - 5 + 3x = 8x - 5
\]

2. Expand the right side:
\[
7(x + 1) = 7x + 7
\]

Now, we can rewrite the equation as:
\[
8x - 5 = 7x + 7
\]

Next, let's isolate \( x \). Start by subtracting \( 7x \) from both sides:
\[
8x - 7x - 5 = 7
\]
This simplifies to:
\[
x - 5 = 7
\]

Now, add \( 5 \) to both sides:
\[
x = 7 + 5
\]
Which gives:
\[
x = 12
\]

So the solution to the equation is:
\[
\boxed{12}
\]