Solve for b 1/2*(b-3)=5/2

$\frac{1}{2} \cdot (b - 3) = \frac{5}{2}$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (b - 3)) = 2 (\frac{5}{2})$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (b - 3))$ .

Apply the distributive property.

$2 (\frac{1}{2} b + \frac{1}{2} \cdot - 3) = 2 (\frac{5}{2})$

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

$2 (\frac{b}{2} + \frac{1}{2} \cdot - 3) = 2 (\frac{5}{2})$

Combine $\frac{1}{2}$ and $- 3$ .

$2 (\frac{b}{2} + \frac{- 3}{2}) = 2 (\frac{5}{2})$

Move the negative in front of the fraction.

$2 (\frac{b}{2} - \frac{3}{2}) = 2 (\frac{5}{2})$

Apply the distributive property.

$2 \frac{b}{2} + 2 (- \frac{3}{2}) = 2 (\frac{5}{2})$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{b}{2} + 2 (- \frac{3}{2}) = 2 (\frac{5}{2})$

Rewrite the expression.

$b + 2 (- \frac{3}{2}) = 2 (\frac{5}{2})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$b + 2 (\frac{- 3}{2}) = 2 (\frac{5}{2})$

Cancel the common factor.

$b + 2 (\frac{- 3}{2}) = 2 (\frac{5}{2})$

Rewrite the expression.

$b - 3 = 2 (\frac{5}{2})$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$b - 3 = 2 (\frac{5}{2})$

Rewrite the expression.

$b - 3 = 5$

Step 3

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

Add $3$ to both sides of the equation.

$b = 5 + 3$

Add $5$ and $3$ .

$b = 8$