Algebra Examples

$\frac{1}{6} (- 4 x - 5) = 6 (2 x + 5)$

Step 1

Simplify $\frac{1}{6} \cdot (- 4 x - 5)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{1}{6} \cdot (- 4 x - 5) = 6 (2 x + 5)$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1

Factor $2$ out of $6$ .

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

Step 1.2.2.2

Factor $2$ out of $- 4 x$ .

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

Step 1.2.2.3

Cancel the common factor.

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

Step 1.2.2.4

Rewrite the expression.

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

Step 1.2.3

Combine $- 2$ and $\frac{1}{3}$ .

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

Step 1.2.4

Combine $\frac{- 2}{3}$ and $x$ .

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

Step 1.2.5

Combine $\frac{1}{6}$ and $- 5$ .

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

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

Move the negative in front of the fraction.

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

Step 1.3.2

Move the negative in front of the fraction.

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

Step 2

Simplify $6 (2 x + 5)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $6$ .

$- \frac{2 x}{3} - \frac{5}{6} = 12 x + 6 \cdot 5$

Step 2.2.2

Multiply $6$ by $5$ .

$- \frac{2 x}{3} - \frac{5}{6} = 12 x + 30$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $12 x$ from both sides of the equation.

$- \frac{2 x}{3} - \frac{5}{6} - 12 x = 30$

Step 3.2

To write $- 12 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 x}{3} - 12 x \cdot \frac{3}{3} - \frac{5}{6} = 30$

Step 3.3

Combine $- 12 x$ and $\frac{3}{3}$ .

$- \frac{2 x}{3} + \frac{- 12 x \cdot 3}{3} - \frac{5}{6} = 30$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 2 x - 12 x \cdot 3}{3} - \frac{5}{6} = 30$

Step 3.5

Simplify each term.

Tap for more steps...

Step 3.5.1

Simplify the numerator.

Tap for more steps...

Step 3.5.1.1

Factor $2 x$ out of $- 2 x - 12 x \cdot 3$ .

Tap for more steps...

Step 3.5.1.1.1

Factor $2 x$ out of $- 2 x$ .

$\frac{2 x (- 1) - 12 x \cdot 3}{3} - \frac{5}{6} = 30$

Step 3.5.1.1.2

Factor $2 x$ out of $- 12 x \cdot 3$ .

$\frac{2 x (- 1) + 2 x (- 6 \cdot 3)}{3} - \frac{5}{6} = 30$

Step 3.5.1.1.3

Factor $2 x$ out of $2 x (- 1) + 2 x (- 6 \cdot 3)$ .

$\frac{2 x (- 1 - 6 \cdot 3)}{3} - \frac{5}{6} = 30$

Step 3.5.1.2

Multiply $- 6$ by $3$ .

$\frac{2 x (- 1 - 18)}{3} - \frac{5}{6} = 30$

Step 3.5.1.3

Subtract $18$ from $- 1$ .

$\frac{2 x \cdot - 19}{3} - \frac{5}{6} = 30$

Step 3.5.1.4

Multiply $- 19$ by $2$ .

$\frac{- 38 x}{3} - \frac{5}{6} = 30$

Step 3.5.2

Move the negative in front of the fraction.

$- \frac{38 x}{3} - \frac{5}{6} = 30$

Step 4

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

Tap for more steps...

Step 4.1

Add $\frac{5}{6}$ to both sides of the equation.

$- \frac{38 x}{3} = 30 + \frac{5}{6}$

Step 4.2

To write $30$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{38 x}{3} = 30 \cdot \frac{6}{6} + \frac{5}{6}$

Step 4.3

Combine $30$ and $\frac{6}{6}$ .

$- \frac{38 x}{3} = \frac{30 \cdot 6}{6} + \frac{5}{6}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{38 x}{3} = \frac{30 \cdot 6 + 5}{6}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $30$ by $6$ .

$- \frac{38 x}{3} = \frac{180 + 5}{6}$

Step 4.5.2

Add $180$ and $5$ .

$- \frac{38 x}{3} = \frac{185}{6}$

Step 5

Multiply both sides of the equation by $- \frac{3}{38}$ .

$- \frac{3}{38} (- \frac{38 x}{3}) = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- \frac{3}{38} (- \frac{38 x}{3})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{3}{38}$ into the numerator.

$\frac{- 3}{38} (- \frac{38 x}{3}) = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.1.2

Move the leading negative in $- \frac{38 x}{3}$ into the numerator.

$\frac{- 3}{38} \cdot \frac{- 38 x}{3} = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{38} \cdot \frac{- 38 x}{3} = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{38} \cdot \frac{- 38 x}{3} = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{38} (- 38 x) = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.2

Cancel the common factor of $38$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $38$ out of $- 38 x$ .

$\frac{- 1}{38} (38 (- x)) = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{38} (38 (- x)) = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{38} \cdot \frac{185}{6}$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- \frac{3}{38} \cdot \frac{185}{6}$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.2.1.1.1

Move the leading negative in $- \frac{3}{38}$ into the numerator.

$x = \frac{- 3}{38} \cdot \frac{185}{6}$

Step 6.2.1.1.2

Factor $3$ out of $- 3$ .

$x = \frac{3 (- 1)}{38} \cdot \frac{185}{6}$

Step 6.2.1.1.3

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 1}{38} \cdot \frac{185}{3 \cdot 2}$

Step 6.2.1.1.4

Cancel the common factor.

$x = \frac{3 \cdot - 1}{38} \cdot \frac{185}{3 \cdot 2}$

Step 6.2.1.1.5

Rewrite the expression.

$x = \frac{- 1}{38} \cdot \frac{185}{2}$

Step 6.2.1.2

Multiply $\frac{- 1}{38}$ by $\frac{185}{2}$ .

$x = \frac{- 1 \cdot 185}{38 \cdot 2}$

Step 6.2.1.3

Simplify the expression.

Tap for more steps...

Step 6.2.1.3.1

Multiply $- 1$ by $185$ .

$x = \frac{- 185}{38 \cdot 2}$

Step 6.2.1.3.2

Multiply $38$ by $2$ .

$x = \frac{- 185}{76}$

Step 6.2.1.3.3

Move the negative in front of the fraction.

$x = - \frac{185}{76}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{185}{76}$

Decimal Form:

$x = - 2.43421052 \dots$

Mixed Number Form:

$x = - 2 \frac{33}{76}$