Algebra Examples

$\frac{x + 2}{3} - \frac{2 x - 4}{2} = 0$

Step 1

Simplify $\frac{x + 2}{3} - \frac{2 x - 4}{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $2 x - 4$ and $2$ .

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Step 1.1.1.1

Factor $2$ out of $2 x$ .

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

Step 1.1.1.2

Factor $2$ out of $- 4$ .

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

Step 1.1.1.3

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

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

Step 1.1.1.4

Cancel the common factors.

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Step 1.1.1.4.1

Factor $2$ out of $2$ .

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

Step 1.1.1.4.2

Cancel the common factor.

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

Step 1.1.1.4.3

Rewrite the expression.

$\frac{x + 2}{3} - \frac{x - 2}{1} = 0$

Step 1.1.1.4.4

Divide $x - 2$ by $1$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Multiply $- 1$ by $- 2$ .

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

Step 1.2

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

$\frac{x + 2}{3} - x \cdot \frac{3}{3} + 2 = 0$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{x + 2}{3} + \frac{- x \cdot 3}{3} + 2 = 0$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{x + 2 - x \cdot 3}{3} + 2 = 0$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $3$ by $- 1$ .

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

Step 1.4.2

Subtract $3 x$ from $x$ .

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

Step 1.4.3

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

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Step 1.4.3.1

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

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

Step 1.4.3.2

Factor $2$ out of $2$ .

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

Step 1.4.3.3

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

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

Step 1.5

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.6

Simplify terms.

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Step 1.6.1

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

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

Step 1.6.2

Combine the numerators over the common denominator.

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

Step 1.7

Simplify the numerator.

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Step 1.7.1

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

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Step 1.7.1.1

Factor $2$ out of $2 \cdot 3$ .

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

Step 1.7.1.2

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

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

Step 1.7.2

Add $1$ and $3$ .

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

Step 1.8

Simplify with factoring out.

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Step 1.8.1

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

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

Step 1.8.2

Rewrite $4$ as $- 1 (- 4)$ .

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

Step 1.8.3

Factor $- 1$ out of $- (x) - 1 (- 4)$ .

$\frac{2 (- (x - 4))}{3} = 0$

Step 1.8.4

Simplify the expression.

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Step 1.8.4.1

Rewrite $- (x - 4)$ as $- 1 (x - 4)$ .

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

Step 1.8.4.2

Move the negative in front of the fraction.

$- \frac{2 (x - 4)}{3} = 0$

Step 2

Set the numerator equal to zero.

$2 (x - 4) = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Divide each term in $2 (x - 4) = 0$ by $2$ and simplify.

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Step 3.1.1

Divide each term in $2 (x - 4) = 0$ by $2$ .

$\frac{2 (x - 4)}{2} = \frac{0}{2}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $2$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{2 (x - 4)}{2} = \frac{0}{2}$

Step 3.1.2.1.2

Divide $x - 4$ by $1$ .

$x - 4 = \frac{0}{2}$

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $0$ by $2$ .

$x - 4 = 0$

Step 3.2

Add $4$ to both sides of the equation.

$x = 4$