Algebra Examples

$\frac{2}{3} (x - 6) = - \frac{1}{3} x - 14$

Step 1

Simplify $\frac{2}{3} \cdot (x - 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (x - 6) = - \frac{1}{3} x - 14$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (x - 6) = - \frac{1}{3} x - 14$

Step 1.3

Apply the distributive property.

$\frac{2}{3} x + \frac{2}{3} \cdot - 6 = - \frac{1}{3} x - 14$

Step 1.4

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

$\frac{2 x}{3} + \frac{2}{3} \cdot - 6 = - \frac{1}{3} x - 14$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 6$ .

$\frac{2 x}{3} + \frac{2}{3} \cdot (3 (- 2)) = - \frac{1}{3} x - 14$

Step 1.5.2

Cancel the common factor.

$\frac{2 x}{3} + \frac{2}{3} \cdot (3 \cdot - 2) = - \frac{1}{3} x - 14$

Step 1.5.3

Rewrite the expression.

$\frac{2 x}{3} + 2 \cdot - 2 = - \frac{1}{3} x - 14$

Step 1.6

Multiply $2$ by $- 2$ .

$\frac{2 x}{3} - 4 = - \frac{1}{3} x - 14$

Step 2

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

$\frac{2 x}{3} - 4 = - \frac{x}{3} - 14$

Step 3

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

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Step 3.1

Add $\frac{x}{3}$ to both sides of the equation.

$\frac{2 x}{3} - 4 + \frac{x}{3} = - 14$

Step 3.2

Combine the numerators over the common denominator.

$- 4 + \frac{2 x + x}{3} = - 14$

Step 3.3

Add $2 x$ and $x$ .

$- 4 + \frac{3 x}{3} = - 14$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$- 4 + \frac{3 x}{3} = - 14$

Step 3.4.2

Divide $x$ by $1$ .

$- 4 + x = - 14$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$x = - 14 + 4$

Step 4.2

Add $- 14$ and $4$ .

$x = - 10$