Algebra Examples

$\frac{3}{5} (x + \frac{1}{6}) = - \frac{23}{10}$

Step 1

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} (\frac{3}{5} \cdot (x + \frac{1}{6})) = \frac{5}{3} (- \frac{23}{10})$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{5}{3} (\frac{3}{5} \cdot (x + \frac{1}{6}))$ .

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

$\frac{5}{3} (\frac{3}{5} x + \frac{3}{5} \cdot \frac{1}{6}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.2

Combine $\frac{3}{5}$ and $x$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{6}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.3.1

Factor $3$ out of $6$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{3 (2)}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{3 \cdot 2}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{5} \cdot \frac{1}{2}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.4

Multiply $\frac{1}{5}$ by $\frac{1}{2}$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{5 \cdot 2}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.5

Multiply $5$ by $2$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{10}) = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.6

Apply the distributive property.

$\frac{5}{3} \cdot \frac{3 x}{5} + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.7

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.7.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 x}{5} + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.7.2

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.8

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.8.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.8.3

Rewrite the expression.

$x + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.9

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.9.1

Factor $5$ out of $10$ .

$x + \frac{5}{3} \cdot \frac{1}{5 (2)} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.9.2

Cancel the common factor.

$x + \frac{5}{3} \cdot \frac{1}{5 \cdot 2} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.9.3

Rewrite the expression.

$x + \frac{1}{3} \cdot \frac{1}{2} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.10

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$x + \frac{1}{3 \cdot 2} = \frac{5}{3} (- \frac{23}{10})$

Step 2.1.1.11

Multiply $3$ by $2$ .

$x + \frac{1}{6} = \frac{5}{3} (- \frac{23}{10})$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $\frac{5}{3} (- \frac{23}{10})$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1.1

Move the leading negative in $- \frac{23}{10}$ into the numerator.

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{10}$

Step 2.2.1.1.2

Factor $5$ out of $10$ .

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{5 (2)}$

Step 2.2.1.1.3

Cancel the common factor.

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{5 \cdot 2}$

Step 2.2.1.1.4

Rewrite the expression.

$x + \frac{1}{6} = \frac{1}{3} \cdot \frac{- 23}{2}$

Step 2.2.1.2

Multiply $\frac{1}{3}$ by $\frac{- 23}{2}$ .

$x + \frac{1}{6} = \frac{- 23}{3 \cdot 2}$

Step 2.2.1.3

Simplify the expression.

Tap for more steps...

Step 2.2.1.3.1

Multiply $3$ by $2$ .

$x + \frac{1}{6} = \frac{- 23}{6}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$x + \frac{1}{6} = - \frac{23}{6}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{1}{6}$ from both sides of the equation.

$x = - \frac{23}{6} - \frac{1}{6}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 23 - 1}{6}$

Step 3.3

Subtract $1$ from $- 23$ .

$x = \frac{- 24}{6}$

Step 3.4

Divide $- 24$ by $6$ .

$x = - 4$