Question

which diagram represents the equation $2r = 16$?
solve for $r$.
$r = \square$

Explanation:

Part 1: Identifying the Correct Diagram

The equation \(2r = 16\) means that the sum of two \(r\) values is 16. In the first diagram, there are two segments labeled \(r\) that add up to 16, which matches the equation. The second diagram has two segments labeled 16 that add up to \(r\) (so \(r = 16 + 16\)), which does not match \(2r = 16\). So the first diagram (with two \(r\)s summing to 16) represents the equation.

Step 1: Start with the equation

We have the equation \(2r = 16\).

Step 2: Isolate \(r\)

To solve for \(r\), we divide both sides of the equation by 2. This is because we want to get \(r\) alone, and since \(r\) is multiplied by 2, we use the inverse operation (division) to undo the multiplication. So we calculate \(\frac{2r}{2}=\frac{16}{2}\).

Step 3: Simplify

Simplifying both sides, the 2 in the numerator and denominator on the left cancels out, leaving \(r\), and on the right, \(\frac{16}{2} = 8\).

Answer:

The first diagram (the one with two purple rectangles labeled \(r\) and the total length 16) represents the equation \(2r = 16\).

Part 2: Solving for \(r\)