Basic Math Examples

$\frac{7}{13} \cdot (w - 1) - \frac{38}{13} = - 3$

Step 1

Simplify $\frac{7}{13} \cdot (w - 1) - \frac{38}{13}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$\frac{7}{13} w + \frac{7}{13} \cdot - 1 - \frac{38}{13} = - 3$

Step 1.1.2

Combine $\frac{7}{13}$ and $w$ .

$\frac{7 w}{13} + \frac{7}{13} \cdot - 1 - \frac{38}{13} = - 3$

Step 1.1.3

Multiply $\frac{7}{13} \cdot - 1$ .

Tap for more steps...

Step 1.1.3.1

Combine $\frac{7}{13}$ and $- 1$ .

$\frac{7 w}{13} + \frac{7 \cdot - 1}{13} - \frac{38}{13} = - 3$

Step 1.1.3.2

Multiply $7$ by $- 1$ .

$\frac{7 w}{13} + \frac{- 7}{13} - \frac{38}{13} = - 3$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{7 w}{13} - \frac{7}{13} - \frac{38}{13} = - 3$

Step 1.2

Combine fractions.

Tap for more steps...

Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 w - 7 - 38}{13} = - 3$

Step 1.2.2

Subtract $38$ from $- 7$ .

$\frac{7 w - 45}{13} = - 3$

Step 2

Multiply both sides by $13$ .

$\frac{7 w - 45}{13} \cdot 13 = - 3 \cdot 13$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $13$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{7 w - 45}{13} \cdot 13 = - 3 \cdot 13$

Step 3.1.1.2

Rewrite the expression.

$7 w - 45 = - 3 \cdot 13$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 3$ by $13$ .

$7 w - 45 = - 39$

Step 4

Solve for $w$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $45$ to both sides of the equation.

$7 w = - 39 + 45$

Step 4.1.2

Add $- 39$ and $45$ .

$7 w = 6$

Step 4.2

Divide each term in $7 w = 6$ by $7$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $7 w = 6$ by $7$ .

$\frac{7 w}{7} = \frac{6}{7}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 w}{7} = \frac{6}{7}$

Step 4.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{6}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = \frac{6}{7}$

Decimal Form:

$w = 0.\overline{857142}$