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?
multiply both sides by 2.
divide both sides by 2.
subtract 2 from both sides.
add 2 to both sides.
(image of hanger with two a weights on left and eight 1 weights on right, and steps 2a + 1 = 9, -1 -1, 2a = 8)

Explanation:

For the first part (writing the equation):

Step1: Analyze the hanger

On the left side, there are 2 weights of \( a \) and 1 weight of 1? Wait, no, looking at the hanger: left has two \( a \) weights, right has 8 (since 4 columns of 2, 42=8) 1 - unit weights? Wait, the equation given is \( 2a + 1 = 9 \)? Wait, maybe the left is \( 2a \) (two \( a \)s) and the right is 8 (since 2a +1 =9, so 9 -1=8, 2a=8). Wait, the first part is to write the equation representing the hanger. From the hanger, left side: two \( a \) weights and maybe 1? Wait, the equation provided is \( 2a + 1 = 9 \), but maybe the correct equation is \( 2a = 8 \)? Wait, no, the image shows the equation \( 2a + 1 = 9 \), and then subtracting 1 from both sides to get \( 2a = 8 \). So the equation representing the hanger is \( 2a + 1 = 9 \) (left: two \( a \)s and 1? Wait, maybe the left has two \( a \)s and the right has 8 ones plus 1? No, the right has 8 ones (4 rows of 2, 42=8), and left has two \( a \)s and 1? Wait, maybe the initial equation is \( 2a + 1 = 9 \), so that's the equation.

For the second part (getting \( a \) by itself):

We have the equation \( 2a + 1 = 9 \). To isolate \( a \), first we can subtract 1 from both sides (as shown in the image: \( 2a + 1 - 1 = 9 - 1 \) → \( 2a = 8 \)), then divide both sides by 2. But among the options, the step after that (or the first step to isolate \( a \) after \( 2a = 8 \)) is to divide both sides by 2. Wait, the options are:

• Multiply both sides by 2: No, that would make \( 4a + 2 = 18 \), not helpful.
• Divide both sides by 2: After we have \( 2a = 8 \) (from subtracting 1), dividing both sides by 2 gives \( a = 4 \). So this is the correct step to get \( a \) by itself (after subtracting 1).
• Subtract 2 from both sides: \( 2a + 1 - 2 = 9 - 2 \) → \( 2a -1 =7 \), not helpful.
• Add 2 to both sides: \( 2a + 1 + 2 = 9 + 2 \) → \( 2a +3 =11 \), not helpful.

So the correct option for "How can you get \( a \) by itself on one side of the equation?" (after getting \( 2a = 8 \)) is to divide both sides by 2.

Answer:

For the equation: \( 2a + 1 = 9 \)
For the second question, the correct option is: Divide both sides by 2. (The option is "Divide both sides by 2.")