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
4(2x+4)
=
2
1
(16x+24)
8x+16
=
2
1
(16x+24)
8x + 16
=
8x + 12
Infinitely many solutions
One solution
No solutions
Answers
GPT-4o mini
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**.
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**.