Algebra Examples

$- \frac{1}{3} (4 x + 2) = \frac{1}{3} (x + 11)$

Step 1

Simplify $- \frac{1}{3} \cdot (4 x + 2)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 - \frac{1}{3} \cdot (4 x + 2) = \frac{1}{3} \cdot (x + 11)$

Step 1.2

Simplify by adding zeros.

$- \frac{1}{3} \cdot (4 x + 2) = \frac{1}{3} \cdot (x + 11)$

Step 1.3

Apply the distributive property.

$- \frac{1}{3} (4 x) - \frac{1}{3} \cdot 2 = \frac{1}{3} \cdot (x + 11)$

Step 1.4

Multiply $- \frac{1}{3} (4 x)$ .

Tap for more steps...

Step 1.4.1

Multiply $4$ by $- 1$ .

$- 4 (\frac{1}{3}) x - \frac{1}{3} \cdot 2 = \frac{1}{3} \cdot (x + 11)$

Step 1.4.2

Combine $- 4$ and $\frac{1}{3}$ .

$\frac{- 4}{3} x - \frac{1}{3} \cdot 2 = \frac{1}{3} \cdot (x + 11)$

Step 1.4.3

Combine $\frac{- 4}{3}$ and $x$ .

$\frac{- 4 x}{3} - \frac{1}{3} \cdot 2 = \frac{1}{3} \cdot (x + 11)$

Step 1.5

Multiply $- \frac{1}{3} \cdot 2$ .

Tap for more steps...

Step 1.5.1

Multiply $2$ by $- 1$ .

$\frac{- 4 x}{3} - 2 (\frac{1}{3}) = \frac{1}{3} \cdot (x + 11)$

Step 1.5.2

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

$\frac{- 4 x}{3} + \frac{- 2}{3} = \frac{1}{3} \cdot (x + 11)$

Step 1.6

Simplify each term.

Tap for more steps...

Step 1.6.1

Move the negative in front of the fraction.

$- \frac{4 x}{3} + \frac{- 2}{3} = \frac{1}{3} \cdot (x + 11)$

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{4 x}{3} - \frac{2}{3} = \frac{1}{3} \cdot (x + 11)$

Step 2

Simplify $\frac{1}{3} \cdot (x + 11)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$- \frac{4 x}{3} - \frac{2}{3} = \frac{1}{3} x + \frac{1}{3} \cdot 11$

Step 2.2

Combine $\frac{1}{3}$ and $x$ .

$- \frac{4 x}{3} - \frac{2}{3} = \frac{x}{3} + \frac{1}{3} \cdot 11$

Step 2.3

Combine $\frac{1}{3}$ and $11$ .

$- \frac{4 x}{3} - \frac{2}{3} = \frac{x}{3} + \frac{11}{3}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{x}{3}$ from both sides of the equation.

$- \frac{4 x}{3} - \frac{2}{3} - \frac{x}{3} = \frac{11}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 4 x - 2 - x}{3} = \frac{11}{3}$

Step 3.3

Subtract $x$ from $- 4 x$ .

$\frac{- 5 x - 2}{3} = \frac{11}{3}$

Step 3.4

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 2}{3} = \frac{11}{3}$

Step 3.5

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (5 x) - 1 (2)}{3} = \frac{11}{3}$

Step 3.6

Factor $- 1$ out of $- (5 x) - 1 (2)$ .

$\frac{- (5 x + 2)}{3} = \frac{11}{3}$

Step 3.7

Rewrite $- (5 x + 2)$ as $- 1 (5 x + 2)$ .

$\frac{- 1 (5 x + 2)}{3} = \frac{11}{3}$

Step 3.8

Move the negative in front of the fraction.

$- \frac{5 x + 2}{3} = \frac{11}{3}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (5 x + 2) = 11$

Step 5

Simplify $- (5 x + 2)$ .

Tap for more steps...

Step 5.1

Apply the distributive property.

$- (5 x) - 1 \cdot 2 = 11$

Step 5.2

Multiply.

Tap for more steps...

Step 5.2.1

Multiply $5$ by $- 1$ .

$- 5 x - 1 \cdot 2 = 11$

Step 5.2.2

Multiply $- 1$ by $2$ .

$- 5 x - 2 = 11$

Step 6

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

Tap for more steps...

Step 6.1

Add $2$ to both sides of the equation.

$- 5 x = 11 + 2$

Step 6.2

Add $11$ and $2$ .

$- 5 x = 13$

Step 7

Divide each term in $- 5 x = 13$ by $- 5$ and simplify.

Tap for more steps...

Step 7.1

Divide each term in $- 5 x = 13$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{13}{- 5}$

Step 7.2

Simplify the left side.

Tap for more steps...

Step 7.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{13}{- 5}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{13}{- 5}$

Step 7.3

Simplify the right side.

Tap for more steps...

Step 7.3.1

Move the negative in front of the fraction.

$x = - \frac{13}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{5}$

Decimal Form:

$x = - 2.6$

Mixed Number Form:

$x = - 2 \frac{3}{5}$