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

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. 
4(2x+4)
=
2
1
​
 (16x+24)
 
8x+16
=
2
1
​
 (16x+24)
 
8x + 16
=
8x + 12

Infinitely many solutions

One solution

No solutions

GPT-4o mini · Answer

Let's analyze the equation step by step.

You have the equation:

$8 x + 16 = 8 x + 12$

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

Subtract $8 x$ from both sides:

$8 x + 16 - 8 x = 8 x + 12 - 8 x$

This simplifies to:

$16 = 12$

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.