Solve for h 3/2(4+1/2h)=1/4(12+6h)

$\frac{3}{2} (4 + \frac{1}{2} h) = \frac{1}{4} (12 + 6 h)$

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

Start simplifying.

$0 + 0 + \frac{3}{2} \cdot (4 + \frac{1}{2} h) = \frac{1}{4} \cdot (12 + 6 h)$

Simplify by adding zeros.

$\frac{3}{2} \cdot (4 + \frac{1}{2} h) = \frac{1}{4} \cdot (12 + 6 h)$

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

$\frac{3}{2} \cdot (4 + \frac{h}{2}) = \frac{1}{4} \cdot (12 + 6 h)$

Apply the distributive property.

$\frac{3}{2} \cdot 4 + \frac{3}{2} \cdot \frac{h}{2} = \frac{1}{4} \cdot (12 + 6 h)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2} \cdot (2 (2)) + \frac{3}{2} \cdot \frac{h}{2} = \frac{1}{4} \cdot (12 + 6 h)$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot 2) + \frac{3}{2} \cdot \frac{h}{2} = \frac{1}{4} \cdot (12 + 6 h)$

Rewrite the expression.

$3 \cdot 2 + \frac{3}{2} \cdot \frac{h}{2} = \frac{1}{4} \cdot (12 + 6 h)$

Multiply $3$ by $2$ .

$6 + \frac{3}{2} \cdot \frac{h}{2} = \frac{1}{4} \cdot (12 + 6 h)$

Multiply $\frac{3}{2} \cdot \frac{h}{2}$ .

Multiply $\frac{3}{2}$ by $\frac{h}{2}$ .

$6 + \frac{3 h}{2 \cdot 2} = \frac{1}{4} \cdot (12 + 6 h)$

Multiply $2$ by $2$ .

$6 + \frac{3 h}{4} = \frac{1}{4} \cdot (12 + 6 h)$

Simplify $\frac{1}{4} \cdot (12 + 6 h)$ .

Apply the distributive property.

$6 + \frac{3 h}{4} = \frac{1}{4} \cdot 12 + \frac{1}{4} (6 h)$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$6 + \frac{3 h}{4} = \frac{1}{4} \cdot (4 (3)) + \frac{1}{4} (6 h)$

Cancel the common factor.

$6 + \frac{3 h}{4} = \frac{1}{4} \cdot (4 \cdot 3) + \frac{1}{4} (6 h)$

Rewrite the expression.

$6 + \frac{3 h}{4} = 3 + \frac{1}{4} (6 h)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$6 + \frac{3 h}{4} = 3 + \frac{1}{2 (2)} (6 h)$

Factor $2$ out of $6 h$ .

$6 + \frac{3 h}{4} = 3 + \frac{1}{2 (2)} (2 (3 h))$

Cancel the common factor.

$6 + \frac{3 h}{4} = 3 + \frac{1}{2 \cdot 2} (2 (3 h))$

Rewrite the expression.

$6 + \frac{3 h}{4} = 3 + \frac{1}{2} (3 h)$

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

$6 + \frac{3 h}{4} = 3 + \frac{3}{2} h$

Combine $\frac{3}{2}$ and $h$ .

$6 + \frac{3 h}{4} = 3 + \frac{3 h}{2}$

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

Subtract $\frac{3 h}{2}$ from both sides of the equation.

$6 + \frac{3 h}{4} - \frac{3 h}{2} = 3$

To write $- \frac{3 h}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 + \frac{3 h}{4} - \frac{3 h}{2} \cdot \frac{2}{2} = 3$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 h}{2}$ by $\frac{2}{2}$ .

$6 + \frac{3 h}{4} - \frac{3 h \cdot 2}{2 \cdot 2} = 3$

Multiply $2$ by $2$ .

$6 + \frac{3 h}{4} - \frac{3 h \cdot 2}{4} = 3$

Combine the numerators over the common denominator.

$6 + \frac{3 h - 3 h \cdot 2}{4} = 3$

Simplify each term.

Simplify the numerator.

Factor $3 h$ out of $3 h - 3 h \cdot 2$ .

Factor $3 h$ out of $3 h$ .

$6 + \frac{3 h (1) - 3 h \cdot 2}{4} = 3$

Factor $3 h$ out of $- 3 h \cdot 2$ .

$6 + \frac{3 h (1) + 3 h (- 1 \cdot 2)}{4} = 3$

Factor $3 h$ out of $3 h (1) + 3 h (- 1 \cdot 2)$ .

$6 + \frac{3 h (1 - 1 \cdot 2)}{4} = 3$

Multiply $- 1$ by $2$ .

$6 + \frac{3 h (1 - 2)}{4} = 3$

Subtract $2$ from $1$ .

$6 + \frac{3 h \cdot - 1}{4} = 3$

Multiply $- 1$ by $3$ .

$6 + \frac{- 3 h}{4} = 3$

Move the negative in front of the fraction.

$6 - \frac{3 h}{4} = 3$

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

Subtract $6$ from both sides of the equation.

$- \frac{3 h}{4} = 3 - 6$

Subtract $6$ from $3$ .

$- \frac{3 h}{4} = - 3$

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 h}{4}) = - \frac{4}{3} \cdot - 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 h}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 h}{4}) = - \frac{4}{3} \cdot - 3$

Move the leading negative in $- \frac{3 h}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 h}{4} = - \frac{4}{3} \cdot - 3$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 h}{4} = - \frac{4}{3} \cdot - 3$

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 h}{4} = - \frac{4}{3} \cdot - 3$

Rewrite the expression.

$\frac{- 1}{3} (- 3 h) = - \frac{4}{3} \cdot - 3$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 h$ .

$\frac{- 1}{3} (3 (- h)) = - \frac{4}{3} \cdot - 3$

Cancel the common factor.

$\frac{- 1}{3} (3 (- h)) = - \frac{4}{3} \cdot - 3$

Rewrite the expression.

$- - h = - \frac{4}{3} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 h = - \frac{4}{3} \cdot - 3$

Multiply $h$ by $1$ .

$h = - \frac{4}{3} \cdot - 3$

Simplify the right side.

Simplify $- \frac{4}{3} \cdot - 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$h = \frac{- 4}{3} \cdot - 3$

Factor $3$ out of $- 3$ .

$h = \frac{- 4}{3} \cdot (3 (- 1))$

Cancel the common factor.

$h = \frac{- 4}{3} \cdot (3 \cdot - 1)$

Rewrite the expression.

$h = - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$h = 4$

Solve for h 3/2(4+1/2h)=1/4(12+6h)

Related Questions

Support LCMGCF.com by disabling your adblocker.