Now that you’ve rewritten both sides of the equation without parentheses, 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.

Question

4(2x+4)
=
2
1
​
(16x+24)

8x+16
=
2
1
​
(16x+24)

8x + 16
=
8x + 12

Infinitely many solutions

One solution

No solutions

Answer 1

Let's analyze the equation step by step.

You have the equation:

\[ 8x + 16 = 8x + 12 \]

To determine how many solutions this equation has, we can isolate \( x \) or simplify the equation.

1. Subtract \( 8x \) from both sides:

\[ 8x + 16 - 8x = 8x + 12 - 8x \]

This simplifies to:

\[ 16 = 12 \]

2. Now we see that \( 16 \) is not equal to \( 12 \). This indicates a contradiction.

Since the simplified equation leads to an inconsistency (16 does not equal 12), the original equation has no solutions.

So the answer is: No solutions.