Solve for b b+3=1/2(b-4)

$b + 3 = \frac{1}{2} (b - 4)$

Step 1

Simplify $\frac{1}{2} \cdot (b - 4)$ .

Rewrite.

$b + 3 = 0 + 0 + \frac{1}{2} \cdot (b - 4)$

Simplify by adding zeros.

$b + 3 = \frac{1}{2} \cdot (b - 4)$

Apply the distributive property.

$b + 3 = \frac{1}{2} b + \frac{1}{2} \cdot - 4$

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

$b + 3 = \frac{b}{2} + \frac{1}{2} \cdot - 4$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$b + 3 = \frac{b}{2} + \frac{1}{2} \cdot (2 (- 2))$

Cancel the common factor.

$b + 3 = \frac{b}{2} + \frac{1}{2} \cdot (2 \cdot - 2)$

Rewrite the expression.

$b + 3 = \frac{b}{2} - 2$

Step 2

Move all terms containing $b$ to the left side of the equation.

Subtract $\frac{b}{2}$ from both sides of the equation.

$b + 3 - \frac{b}{2} = - 2$

To write $b$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b \cdot \frac{2}{2} - \frac{b}{2} + 3 = - 2$

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

$\frac{b \cdot 2}{2} - \frac{b}{2} + 3 = - 2$

Combine the numerators over the common denominator.

$\frac{b \cdot 2 - b}{2} + 3 = - 2$

Subtract $b$ from $b \cdot 2$ .

Reorder $b$ and $2$ .

$\frac{2 \cdot b - b}{2} + 3 = - 2$

Subtract $b$ from $2 \cdot b$ .

$\frac{b}{2} + 3 = - 2$

Step 3

Move all terms not containing $b$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$\frac{b}{2} = - 2 - 3$

Subtract $3$ from $- 2$ .

$\frac{b}{2} = - 5$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{b}{2} = 2 \cdot - 5$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{b}{2} = 2 \cdot - 5$

Rewrite the expression.

$b = 2 \cdot - 5$

Simplify the right side.

Multiply $2$ by $- 5$ .

$b = - 10$

Solve for b b+3=1/2(b-4)

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