Question

write an equation that represents the weights on the hanger. 2a + 1 = 9 how can you get a by itself on one side of the equation? subtract 2 from both sides. multiply both sides by 2. divide both sides by 2. add 2 to both sides.

Explanation:

Part 1: Equation for the hanger (already given as \(2a + 1 = 9\), but let's confirm the process)

The hanger has a side with \(2a + 1\) (representing two weights of \(a\) and one weight of \(1\)) and the other side with \(9\) (representing a weight of \(9\)). Since the hanger is balanced, the equation is \(2a + 1 = 9\).

Part 2: Solving for \(a\) (isolating \(a\))

To isolate \(a\), we first need to get rid of the \(+1\) on the left side. We do this by subtracting \(1\) from both sides (not subtracting 2, multiplying by 2, or adding 2). Wait, the options given are:

• Subtract 2 from both sides.
• Multiply both sides by 2.
• Divide both sides by 2.
• Add 2 to both sides.

Wait, maybe there's a misstep. Wait, the equation is \(2a + 1 = 9\). Let's correct:

First, subtract 1 from both sides: \(2a + 1 - 1 = 9 - 1\) → \(2a = 8\). Then, divide both sides by 2: \(\frac{2a}{2} = \frac{8}{2}\) → \(a = 4\).

Looking at the options, "Divide both sides by 2" is a step (after subtracting 1, but maybe the question is about the second step). Let's check the options:

• Subtract 2 from both sides: Incorrect, we need to subtract 1 first.
• Multiply both sides by 2: Incorrect, that would make \(4a + 2 = 18\), worse.
• Divide both sides by 2: After subtracting 1, this is the next step. So this is a valid step to get \(a + \frac{1}{2} = \frac{9}{2}\)? No, wait, original equation \(2a + 1 = 9\). If we divide both sides by 2 first: \(a + \frac{1}{2} = \frac{9}{2}\), then subtract \(\frac{1}{2}\) from both sides: \(a = \frac{9}{2} - \frac{1}{2} = 4\). So dividing both sides by 2 is a valid step (even if it's not the first step, it's a step to get \(a\) closer to being isolated).

• Add 2 to both sides: Incorrect, that would make \(2a + 3 = 11\), worse.

So the correct option is "Divide both sides by 2" (option 3: Divide both sides by 2).

Answer:

(for the second part):
C. Divide both sides by 2 (assuming the options are labeled as A: Subtract 2..., B: Multiply..., C: Divide..., D: Add...; if the options are as given, the third option: "Divide both sides by 2")