Questions: Solve for (b). [ r=2(b+a) b=square ]

Solve for (b). [ r=2(b+a) b=square ]
Transcript text: Solve for $b$. \[ \begin{array}{l} r=2(b+a) \\ b=\square \end{array} \] Explanation Check
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Solution

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Solution Steps

To solve for \( b \) in the equation \( r = 2(b + a) \), we need to isolate \( b \) on one side of the equation. This can be done by first dividing both sides by 2 to get rid of the coefficient in front of the parentheses, and then subtracting \( a \) from both sides to solve for \( b \).

Step 1: Isolate the Expression for \( b \)

Given the equation:

\[ r = 2(b + a) \]

First, divide both sides by 2 to eliminate the coefficient in front of the parentheses:

\[ \frac{r}{2} = b + a \]

Step 2: Solve for \( b \)

Next, subtract \( a \) from both sides to isolate \( b \):

\[ b = \frac{r}{2} - a \]

Step 3: Substitute the Given Values

Substitute the given values \( r = 10 \) and \( a = 3 \) into the equation:

\[ b = \frac{10}{2} - 3 \]

Step 4: Simplify the Expression

Calculate the expression:

\[ b = 5 - 3 = 2 \]

Final Answer

The value of \( b \) is \(\boxed{2}\).

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