Question

Now that you’ve rewritten both sides of the equation, take a look. How many solutions does this equation have? You may consider either using the structure of the equation or trying to isolate x on paper to help you figure out how many solutions this equation has.
5x+3x+6
=
4(2x+6)

5x+3x+6
=
8x + 24

8x + 6
=
8x + 24

No solutions

One solution

Infinitely many solutions

Answer 1

Let's analyze the rewritten equation step by step:

You started with the equation:

\[ 5x + 3x + 6 = 4(2x + 6) \]

You then simplified the left side:

\[ 8x + 6 = 4(2x + 6) \]

Next, you simplified the right side:

\[ 8x + 6 = 8x + 24 \]

Now, let's work with the simplified equation:

\[ 8x + 6 = 8x + 24 \]

If we try to isolate \( x \) by subtracting \( 8x \) from both sides, we get:

\[ 6 = 24 \]

This is a contradiction, as 6 does not equal 24.

This indicates that there are no values of \( x \) that would satisfy the original equation.

Therefore, the conclusion is:

**No solutions.**