Solve for h 1/2(5-2h)=h/2

$\frac{1}{2} (5 - 2 h) = \frac{h}{2}$

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{1}{2} \cdot (5 - 2 h) \cdot 2$ .

Apply the distributive property.

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

Combine $\frac{1}{2}$ and $5$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 h$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(\frac{5}{2} - h) \cdot 2 = \frac{h}{2} \cdot 2$

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Multiply $2$ by $- 1$ .

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

Reorder $5$ and $- 2 h$ .

$- 2 h + 5 = \frac{h}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$- 2 h + 5 = \frac{h}{2} \cdot 2$

Rewrite the expression.

$- 2 h + 5 = h$

Step 3

Solve for $h$ .

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

Subtract $h$ from both sides of the equation.

$- 2 h + 5 - h = 0$

Subtract $h$ from $- 2 h$ .

$- 3 h + 5 = 0$

Subtract $5$ from both sides of the equation.

$- 3 h = - 5$

Divide each term in $- 3 h = - 5$ by $- 3$ and simplify.

Divide each term in $- 3 h = - 5$ by $- 3$ .

$\frac{- 3 h}{- 3} = \frac{- 5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 h}{- 3} = \frac{- 5}{- 3}$

Divide $h$ by $1$ .

$h = \frac{- 5}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$h = \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$h = \frac{5}{3}$

Decimal Form:

$h = 1.\overline{6}$

Mixed Number Form:

$h = 1 \frac{2}{3}$

Solve for h 1/2(5-2h)=h/2

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