Algebra Examples

$16 = \frac{1}{2} \cdot 4 (3 + b_{2})$

Step 1

Since $b_{2}$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{1}{2} \cdot (4 (3 + b_{2})) = 16$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{2} \cdot 4}$ .

$\frac{1}{\frac{1}{2} \cdot 4} (\frac{1}{2} \cdot (4 (3 + b_{2}))) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{1}{\frac{1}{2} \cdot 4} (\frac{1}{2} \cdot (4 (3 + b_{2})))$ .

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Step 3.1.1.1

Combine $\frac{1}{2}$ and $4$ .

$\frac{1}{\frac{4}{2}} (\frac{1}{2} \cdot (4 (3 + b_{2}))) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.2

Divide $4$ by $2$ .

$\frac{1}{2} (\frac{1}{2} \cdot (4 (3 + b_{2}))) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Factor $2$ out of $\frac{1}{2} \cdot (4 (3 + b_{2}))$ .

$\frac{1}{2} (2 (\frac{1}{2} \cdot (2 (3 + b_{2})))) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 (\frac{1}{2} \cdot (2 (3 + b_{2})))) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{1}{2} \cdot (2 (3 + b_{2})) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.4

Combine $2$ and $\frac{1}{2}$ .

$\frac{2}{2} \cdot (3 + b_{2}) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.5

Simplify the expression.

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Step 3.1.1.5.1

Divide $2$ by $2$ .

$1 \cdot (3 + b_{2}) = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.1.1.5.2

Multiply $3 + b_{2}$ by $1$ .

$3 + b_{2} = \frac{1}{\frac{1}{2} \cdot 4} \cdot 16$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1}{2} \cdot 4} \cdot 16$ .

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Step 3.2.1.1

Combine $\frac{1}{2}$ and $4$ .

$3 + b_{2} = \frac{1}{\frac{4}{2}} \cdot 16$

Step 3.2.1.2

Divide $4$ by $2$ .

$3 + b_{2} = \frac{1}{2} \cdot 16$

Step 3.2.1.3

Cancel the common factor of $2$ .

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Step 3.2.1.3.1

Factor $2$ out of $16$ .

$3 + b_{2} = \frac{1}{2} \cdot (2 (8))$

Step 3.2.1.3.2

Cancel the common factor.

$3 + b_{2} = \frac{1}{2} \cdot (2 \cdot 8)$

Step 3.2.1.3.3

Rewrite the expression.

$3 + b_{2} = 8$

Step 4

Move all terms not containing $b_{2}$ to the right side of the equation.

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Step 4.1

Subtract $3$ from both sides of the equation.

$b_{2} = 8 - 3$

Step 4.2

Subtract $3$ from $8$ .

$b_{2} = 5$