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) = 1/2(16x+24)
8x+16 = 1/2 (16x+24)
8x + 16 = ? + ?

Answer 1

Let's start with rewriting the equation step-by-step.

The original equation is: \[ 4(2x + 4) = \frac{1}{2}(16x + 24) \]

First, we'll distribute both sides:

1. Left side: \[ 4(2x + 4) = 4 \cdot 2x + 4 \cdot 4 = 8x + 16 \]

2. Right side: \[ \frac{1}{2}(16x + 24) = \frac{1}{2} \cdot 16x + \frac{1}{2} \cdot 24 = 8x + 12 \]

Now, we can rewrite the equation without parentheses:

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

Next, to isolate \(x\), we can subtract \(8x\) from both sides:

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

This simplifies to:

\[ 16 = 12 \]

This statement is a contradiction, as \(16\) does not equal \(12\).

Since we reached a contradiction, the original equation has no solutions.