Basic Math Examples

$\frac{8 h - 7}{3} + \frac{4 (2 h - 5)}{6} - 1 = \frac{7 h - 4}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{8 h - 7}{3} + \frac{4 (2 h - 5)}{6} - 1) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $(\frac{8 h - 7}{3} + \frac{4 (2 h - 5)}{6} - 1) \cdot 2$ .

Tap for more steps...

Step 2.1.1.1

Find the common denominator.

Tap for more steps...

Step 2.1.1.1.1

Multiply $\frac{8 h - 7}{3}$ by $\frac{2}{2}$ .

$(\frac{8 h - 7}{3} \cdot \frac{2}{2} + \frac{4 (2 h - 5)}{6} - 1) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.2

Multiply $\frac{8 h - 7}{3}$ by $\frac{2}{2}$ .

$(\frac{(8 h - 7) \cdot 2}{3 \cdot 2} + \frac{4 (2 h - 5)}{6} - 1) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.3

Write $- 1$ as a fraction with denominator $1$ .

$(\frac{(8 h - 7) \cdot 2}{3 \cdot 2} + \frac{4 (2 h - 5)}{6} + \frac{- 1}{1}) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.4

Multiply $\frac{- 1}{1}$ by $\frac{6}{6}$ .

$(\frac{(8 h - 7) \cdot 2}{3 \cdot 2} + \frac{4 (2 h - 5)}{6} + \frac{- 1}{1} \cdot \frac{6}{6}) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.5

Multiply $\frac{- 1}{1}$ by $\frac{6}{6}$ .

$(\frac{(8 h - 7) \cdot 2}{3 \cdot 2} + \frac{4 (2 h - 5)}{6} + \frac{- 1 \cdot 6}{6}) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.6

Reorder the factors of $3 \cdot 2$ .

$(\frac{(8 h - 7) \cdot 2}{2 \cdot 3} + \frac{4 (2 h - 5)}{6} + \frac{- 1 \cdot 6}{6}) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.1.7

Multiply $2$ by $3$ .

$(\frac{(8 h - 7) \cdot 2}{6} + \frac{4 (2 h - 5)}{6} + \frac{- 1 \cdot 6}{6}) \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.2

Combine the numerators over the common denominator.

$\frac{(8 h - 7) \cdot 2 + 4 (2 h - 5) - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3

Simplify each term.

Tap for more steps...

Step 2.1.1.3.1

Apply the distributive property.

$\frac{8 h \cdot 2 - 7 \cdot 2 + 4 (2 h - 5) - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.2

Multiply $2$ by $8$ .

$\frac{16 h - 7 \cdot 2 + 4 (2 h - 5) - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.3

Multiply $- 7$ by $2$ .

$\frac{16 h - 14 + 4 (2 h - 5) - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.4

Apply the distributive property.

$\frac{16 h - 14 + 4 (2 h) + 4 \cdot - 5 - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.5

Multiply $2$ by $4$ .

$\frac{16 h - 14 + 8 h + 4 \cdot - 5 - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.6

Multiply $4$ by $- 5$ .

$\frac{16 h - 14 + 8 h - 20 - 1 \cdot 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.3.7

Multiply $- 1$ by $6$ .

$\frac{16 h - 14 + 8 h - 20 - 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4

Simplify terms.

Tap for more steps...

Step 2.1.1.4.1

Add $16 h$ and $8 h$ .

$\frac{24 h - 14 - 20 - 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.2

Simplify by subtracting numbers.

Tap for more steps...

Step 2.1.1.4.2.1

Subtract $20$ from $- 14$ .

$\frac{24 h - 34 - 6}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.2.2

Subtract $6$ from $- 34$ .

$\frac{24 h - 40}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.3

Factor $8$ out of $24 h - 40$ .

Tap for more steps...

Step 2.1.1.4.3.1

Factor $8$ out of $24 h$ .

$\frac{8 (3 h) - 40}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.3.2

Factor $8$ out of $- 40$ .

$\frac{8 (3 h) + 8 (- 5)}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.3.3

Factor $8$ out of $8 (3 h) + 8 (- 5)$ .

$\frac{8 (3 h - 5)}{6} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.4.4.1

Factor $2$ out of $6$ .

$\frac{8 (3 h - 5)}{2 (3)} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.4.2

Cancel the common factor.

$\frac{8 (3 h - 5)}{2 \cdot 3} \cdot 2 = \frac{7 h - 4}{2} \cdot 2$

Step 2.1.1.4.4.3

Rewrite the expression.

$\frac{8 (3 h - 5)}{3} = \frac{7 h - 4}{2} \cdot 2$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{8 (3 h - 5)}{3} = \frac{7 h - 4}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{8 (3 h - 5)}{3} = 7 h - 4$

Step 3

Solve for $h$ .

Tap for more steps...

Step 3.1

Multiply both sides by $3$ .

$\frac{8 (3 h - 5)}{3} \cdot 3 = (7 h - 4) \cdot 3$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify $\frac{8 (3 h - 5)}{3} \cdot 3$ .

Tap for more steps...

Step 3.2.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{8 (3 h - 5)}{3} \cdot 3 = (7 h - 4) \cdot 3$

Step 3.2.1.1.1.2

Rewrite the expression.

$8 (3 h - 5) = (7 h - 4) \cdot 3$

Step 3.2.1.1.2

Apply the distributive property.

$8 (3 h) + 8 \cdot - 5 = (7 h - 4) \cdot 3$

Step 3.2.1.1.3

Multiply.

Tap for more steps...

Step 3.2.1.1.3.1

Multiply $3$ by $8$ .

$24 h + 8 \cdot - 5 = (7 h - 4) \cdot 3$

Step 3.2.1.1.3.2

Multiply $8$ by $- 5$ .

$24 h - 40 = (7 h - 4) \cdot 3$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Simplify $(7 h - 4) \cdot 3$ .

Tap for more steps...

Step 3.2.2.1.1

Apply the distributive property.

$24 h - 40 = 7 h \cdot 3 - 4 \cdot 3$

Step 3.2.2.1.2

Multiply.

Tap for more steps...

Step 3.2.2.1.2.1

Multiply $3$ by $7$ .

$24 h - 40 = 21 h - 4 \cdot 3$

Step 3.2.2.1.2.2

Multiply $- 4$ by $3$ .

$24 h - 40 = 21 h - 12$

Step 3.3

Solve for $h$ .

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

Subtract $21 h$ from both sides of the equation.

$24 h - 40 - 21 h = - 12$

Step 3.3.1.2

Subtract $21 h$ from $24 h$ .

$3 h - 40 = - 12$

Step 3.3.2

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

Tap for more steps...

Step 3.3.2.1

Add $40$ to both sides of the equation.

$3 h = - 12 + 40$

Step 3.3.2.2

Add $- 12$ and $40$ .

$3 h = 28$

Step 3.3.3

Divide each term in $3 h = 28$ by $3$ and simplify.

Tap for more steps...

Step 3.3.3.1

Divide each term in $3 h = 28$ by $3$ .

$\frac{3 h}{3} = \frac{28}{3}$

Step 3.3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{3 h}{3} = \frac{28}{3}$

Step 3.3.3.2.1.2

Divide $h$ by $1$ .

$h = \frac{28}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$h = \frac{28}{3}$

Decimal Form:

$h = 9.\overline{3}$

Mixed Number Form:

$h = 9 \frac{1}{3}$