First, let’s try to isolate the variable, x. Right now, x is inside parentheses on the left and right sides. Start by looking at the left side. How could we rewrite the left side of the equation without parentheses so that it’s easier to work with?

Question

4(2x+4) = 1/2 (16x+24)

Add 4 to each side

Add 2x to each side

Distribute the 4 to the 2x and to the 4

Answer 1

To isolate the variable \( x \), we want to simplify the equation by eliminating parentheses. The left side of the equation is currently written as \( 4(2x + 4) \). To rewrite this without parentheses, we need to distribute the \( 4 \) to both terms inside the parentheses:

• Distributing the \( 4 \) gives us: \[ 4 \cdot 2x + 4 \cdot 4 = 8x + 16 \]

So, the left side \( 4(2x + 4) \) becomes \( 8x + 16 \).

Now, we can rewrite the entire equation: \[ 8x + 16 = \frac{1}{2}(16x + 24) \]

Next, we can simplify the right side as well. We can distribute \( \frac{1}{2} \): \[ \frac{1}{2} \cdot 16x + \frac{1}{2} \cdot 24 = 8x + 12 \]

Now we have: \[ 8x + 16 = 8x + 12 \]

Next, we can proceed to isolate \( x \) or analyze further. Would you like to continue solving for \( x \)?