Algebra Examples

$- \frac{1}{8} (2 h + 4) + \frac{1}{2} = - \frac{7}{4}$

Step 1

Simplify $- \frac{1}{8} \cdot (2 h + 4) + \frac{1}{2}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$- \frac{1}{8} (2 h) - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.2.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{- 1}{8} (2 h) - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.2.2

Factor $2$ out of $8$ .

$\frac{- 1}{2 (4)} (2 h) - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.2.3

Factor $2$ out of $2 h$ .

$\frac{- 1}{2 (4)} (2 (h)) - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.2.4

Cancel the common factor.

$\frac{- 1}{2 \cdot 4} (2 h) - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.2.5

Rewrite the expression.

$\frac{- 1}{4} h - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.3

Combine $\frac{- 1}{4}$ and $h$ .

$\frac{- h}{4} - \frac{1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.1.4.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{- h}{4} + \frac{- 1}{8} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.4.2

Factor $4$ out of $8$ .

$\frac{- h}{4} + \frac{- 1}{4 (2)} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.4.3

Cancel the common factor.

$\frac{- h}{4} + \frac{- 1}{4 \cdot 2} \cdot 4 + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.4.4

Rewrite the expression.

$\frac{- h}{4} + \frac{- 1}{2} + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.5

Simplify each term.

Tap for more steps...

Step 1.1.5.1

Move the negative in front of the fraction.

$- \frac{h}{4} + \frac{- 1}{2} + \frac{1}{2} = - \frac{7}{4}$

Step 1.1.5.2

Move the negative in front of the fraction.

$- \frac{h}{4} - \frac{1}{2} + \frac{1}{2} = - \frac{7}{4}$

Step 1.2

Combine the opposite terms in $- \frac{h}{4} - \frac{1}{2} + \frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

Add $- \frac{1}{2}$ and $\frac{1}{2}$ .

$- \frac{h}{4} + 0 = - \frac{7}{4}$

Step 1.2.2

Add $- \frac{h}{4}$ and $0$ .

$- \frac{h}{4} = - \frac{7}{4}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- h = - 7$

Step 3

Divide each term in $- h = - 7$ by $- 1$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- h = - 7$ by $- 1$ .

$\frac{- h}{- 1} = \frac{- 7}{- 1}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{h}{1} = \frac{- 7}{- 1}$

Step 3.2.2

Divide $h$ by $1$ .

$h = \frac{- 7}{- 1}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $- 7$ by $- 1$ .

$h = 7$