Question

what equation represents the weights shown on the hanger?
2a + 1 = 9
how can you isolate the variable term 2a?
divide both sides by 2.
add 1 to both sides.
subtract 1 from both sides.
multiply both sides by 2.
2a + 1 = 9

Explanation:

First Sub - Question (Equation for Hanger Weights)

Step 1: Analyze left - hand side of the hanger

On the left - hand side of the hanger, we have two weights of value \(a\) and one weight of value \(1\). So the total weight on the left is \(a + a+1=2a + 1\).

Step 2: Analyze right - hand side of the hanger

On the right - hand side, we can count the number of weights with value \(1\). Let's count them: there are 9 weights of value \(1\), so the total weight on the right is \(9\).
Since the hanger is in balance, the weight on the left is equal to the weight on the right. So the equation is \(2a + 1=9\).

To isolate the variable term \(2a\) in the equation \(2a + 1=9\), we use the subtraction property of equality. The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true. We want to get rid of the \(+ 1\) on the left - hand side. So we subtract \(1\) from both sides of the equation \(2a+1 = 9\). When we do this, the left - hand side becomes \(2a+1 - 1=2a\) and the right - hand side becomes \(9 - 1 = 8\), and we are left with \(2a=8\), which means we have isolated \(2a\).

Answer:

\(2a + 1 = 9\)

Second Sub - Question (Isolating \(2a\))