Finite Math Examples

$64 = \frac{5}{9} \cdot (x - 32)$

Step 1

Rewrite the equation as $\frac{5}{9} \cdot (x - 32) = 64$ .

$\frac{5}{9} \cdot (x - 32) = 64$

Step 2

Multiply both sides of the equation by $\frac{9}{5}$ .

$\frac{9}{5} (\frac{5}{9} \cdot (x - 32)) = \frac{9}{5} \cdot 64$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{9}{5} (\frac{5}{9} \cdot (x - 32))$ .

Tap for more steps...

Step 3.1.1.1

Apply the distributive property.

$\frac{9}{5} (\frac{5}{9} x + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 64$

Step 3.1.1.2

Combine $\frac{5}{9}$ and $x$ .

$\frac{9}{5} (\frac{5 x}{9} + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 64$

Step 3.1.1.3

Multiply $\frac{5}{9} \cdot - 32$ .

Tap for more steps...

Step 3.1.1.3.1

Combine $\frac{5}{9}$ and $- 32$ .

$\frac{9}{5} (\frac{5 x}{9} + \frac{5 \cdot - 32}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.3.2

Multiply $5$ by $- 32$ .

$\frac{9}{5} (\frac{5 x}{9} + \frac{- 160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.4

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 x}{9} - \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.5

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 x}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.6

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.1.1.6.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 x}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 x) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.7

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.1.1.7.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.7.3

Rewrite the expression.

$x + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 64$

Step 3.1.1.8

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.1.1.8.1

Move the leading negative in $- \frac{160}{9}$ into the numerator.

$x + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 64$

Step 3.1.1.8.2

Cancel the common factor.

$x + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 64$

Step 3.1.1.8.3

Rewrite the expression.

$x + \frac{1}{5} \cdot - 160 = \frac{9}{5} \cdot 64$

Step 3.1.1.9

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.1.1.9.1

Factor $5$ out of $- 160$ .

$x + \frac{1}{5} \cdot (5 (- 32)) = \frac{9}{5} \cdot 64$

Step 3.1.1.9.2

Cancel the common factor.

$x + \frac{1}{5} \cdot (5 \cdot - 32) = \frac{9}{5} \cdot 64$

Step 3.1.1.9.3

Rewrite the expression.

$x - 32 = \frac{9}{5} \cdot 64$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $\frac{9}{5} \cdot 64$ .

Tap for more steps...

Step 3.2.1.1

Combine $\frac{9}{5}$ and $64$ .

$x - 32 = \frac{9 \cdot 64}{5}$

Step 3.2.1.2

Multiply $9$ by $64$ .

$x - 32 = \frac{576}{5}$

Step 4

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

Tap for more steps...

Step 4.1

Add $32$ to both sides of the equation.

$x = \frac{576}{5} + 32$

Step 4.2

To write $32$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{576}{5} + 32 \cdot \frac{5}{5}$

Step 4.3

Combine $32$ and $\frac{5}{5}$ .

$x = \frac{576}{5} + \frac{32 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{576 + 32 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $32$ by $5$ .

$x = \frac{576 + 160}{5}$

Step 4.5.2

Add $576$ and $160$ .

$x = \frac{736}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{736}{5}$

Decimal Form:

$x = 147.2$

Mixed Number Form:

$x = 147 \frac{1}{5}$