Question

1. what is the solution to the equation 5(2w + 4) = 4(2w + 9)?

options:

• w = 5/2
• w = 8
• w = 28/9
• w = 5

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left side \(5(2w + 4)\) to get \(5\times2w+5\times4 = 10w + 20\), and the right side \(4(2w + 9)\) to get \(4\times2w+4\times9=8w + 36\). So the equation becomes \(10w + 20=8w + 36\).

Step2: Subtract \(8w\) from both sides

Subtracting \(8w\) from both sides of the equation \(10w + 20=8w + 36\), we have \(10w-8w + 20=8w-8w + 36\), which simplifies to \(2w+20 = 36\).

Step3: Subtract 20 from both sides

Subtracting 20 from both sides of \(2w+20 = 36\), we get \(2w+20 - 20=36 - 20\), so \(2w=16\).

Step4: Divide both sides by 2

Dividing both sides of \(2w=16\) by 2, we have \(\frac{2w}{2}=\frac{16}{2}\), which gives \(w = 8\).

Answer:

B. \(w = 8\) (assuming the second option is labeled as B, if we follow the standard multiple - choice labeling where the first option is A, second is B, etc. Here the second option is \(w = 8\))