Algebra Examples

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

Step 1

Simplify $\frac{1}{3} \cdot (10 + x)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (10 + x) = x$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

$\frac{1}{3} \cdot 10 + \frac{1}{3} x = x$

Step 1.4

Combine $\frac{1}{3}$ and $10$ .

$\frac{10}{3} + \frac{1}{3} x = x$

Step 1.5

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

$\frac{10}{3} + \frac{x}{3} = x$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{10}{3} + \frac{x}{3} - x = 0$

Step 2.2

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

$\frac{10}{3} + \frac{x}{3} - x \cdot \frac{3}{3} = 0$

Step 2.3

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

$\frac{10}{3} + \frac{x}{3} + \frac{- x \cdot 3}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{10}{3} + \frac{x - x \cdot 3}{3} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{10 + x - x \cdot 3}{3} = 0$

Step 2.6

Multiply $3$ by $- 1$ .

$\frac{10 + x - 3 x}{3} = 0$

Step 2.7

Subtract $3 x$ from $x$ .

$\frac{10 - 2 x}{3} = 0$

Step 2.8

Factor $2$ out of $10 - 2 x$ .

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Step 2.8.1

Factor $2$ out of $10$ .

$\frac{2 (5) - 2 x}{3} = 0$

Step 2.8.2

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

$\frac{2 (5) + 2 (- x)}{3} = 0$

Step 2.8.3

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

$\frac{2 (5 - x)}{3} = 0$

Step 3

Set the numerator equal to zero.

$2 (5 - x) = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Divide each term in $2 (5 - x) = 0$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 (5 - x) = 0$ by $2$ .

$\frac{2 (5 - x)}{2} = \frac{0}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (5 - x)}{2} = \frac{0}{2}$

Step 4.1.2.1.2

Divide $5 - x$ by $1$ .

$5 - x = \frac{0}{2}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $2$ .

$5 - x = 0$

Step 4.2

Subtract $5$ from both sides of the equation.

$- x = - 5$

Step 4.3

Divide each term in $- x = - 5$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 5$ by $- 1$ .

$x = 5$