Algebra Examples

$\frac{x + 6}{2} + \frac{5 - 4 x}{3} - \frac{8 - x}{6} = 0$

Step 1

Simplify $\frac{x + 6}{2} + \frac{5 - 4 x}{3} - \frac{8 - x}{6}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{x + 6}{2}$ by $\frac{3}{3}$ .

$\frac{x + 6}{2} \cdot \frac{3}{3} + \frac{5 - 4 x}{3} - \frac{8 - x}{6} = 0$

Step 1.1.2

Multiply $\frac{x + 6}{2}$ by $\frac{3}{3}$ .

$\frac{(x + 6) \cdot 3}{2 \cdot 3} + \frac{5 - 4 x}{3} - \frac{8 - x}{6} = 0$

Step 1.1.3

Multiply $\frac{5 - 4 x}{3}$ by $\frac{2}{2}$ .

$\frac{(x + 6) \cdot 3}{2 \cdot 3} + \frac{5 - 4 x}{3} \cdot \frac{2}{2} - \frac{8 - x}{6} = 0$

Step 1.1.4

Multiply $\frac{5 - 4 x}{3}$ by $\frac{2}{2}$ .

$\frac{(x + 6) \cdot 3}{2 \cdot 3} + \frac{(5 - 4 x) \cdot 2}{3 \cdot 2} - \frac{8 - x}{6} = 0$

Step 1.1.5

Multiply $2$ by $3$ .

$\frac{(x + 6) \cdot 3}{6} + \frac{(5 - 4 x) \cdot 2}{3 \cdot 2} - \frac{8 - x}{6} = 0$

Step 1.1.6

Reorder the factors of $3 \cdot 2$ .

$\frac{(x + 6) \cdot 3}{6} + \frac{(5 - 4 x) \cdot 2}{2 \cdot 3} - \frac{8 - x}{6} = 0$

Step 1.1.7

Multiply $2$ by $3$ .

$\frac{(x + 6) \cdot 3}{6} + \frac{(5 - 4 x) \cdot 2}{6} - \frac{8 - x}{6} = 0$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(x + 6) \cdot 3 + (5 - 4 x) \cdot 2 - (8 - x)}{6} = 0$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{x \cdot 3 + 6 \cdot 3 + (5 - 4 x) \cdot 2 - (8 - x)}{6} = 0$

Step 1.3.2

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 6 \cdot 3 + (5 - 4 x) \cdot 2 - (8 - x)}{6} = 0$

Step 1.3.3

Multiply $6$ by $3$ .

$\frac{3 \cdot x + 18 + (5 - 4 x) \cdot 2 - (8 - x)}{6} = 0$

Step 1.3.4

Apply the distributive property.

$\frac{3 x + 18 + 5 \cdot 2 - 4 x \cdot 2 - (8 - x)}{6} = 0$

Step 1.3.5

Multiply $5$ by $2$ .

$\frac{3 x + 18 + 10 - 4 x \cdot 2 - (8 - x)}{6} = 0$

Step 1.3.6

Multiply $2$ by $- 4$ .

$\frac{3 x + 18 + 10 - 8 x - (8 - x)}{6} = 0$

Step 1.3.7

Apply the distributive property.

$\frac{3 x + 18 + 10 - 8 x - 1 \cdot 8 - - x}{6} = 0$

Step 1.3.8

Multiply $- 1$ by $8$ .

$\frac{3 x + 18 + 10 - 8 x - 8 - - x}{6} = 0$

Step 1.3.9

Multiply $- - x$ .

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Step 1.3.9.1

Multiply $- 1$ by $- 1$ .

$\frac{3 x + 18 + 10 - 8 x - 8 + 1 x}{6} = 0$

Step 1.3.9.2

Multiply $x$ by $1$ .

$\frac{3 x + 18 + 10 - 8 x - 8 + x}{6} = 0$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $8 x$ from $3 x$ .

$\frac{- 5 x + 18 + 10 - 8 + x}{6} = 0$

Step 1.4.2

Add $- 5 x$ and $x$ .

$\frac{- 4 x + 18 + 10 - 8}{6} = 0$

Step 1.4.3

Simplify by adding and subtracting.

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Step 1.4.3.1

Add $18$ and $10$ .

$\frac{- 4 x + 28 - 8}{6} = 0$

Step 1.4.3.2

Subtract $8$ from $28$ .

$\frac{- 4 x + 20}{6} = 0$

Step 1.4.4

Cancel the common factor of $- 4 x + 20$ and $6$ .

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Step 1.4.4.1

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

$\frac{2 (- 2 x) + 20}{6} = 0$

Step 1.4.4.2

Factor $2$ out of $20$ .

$\frac{2 (- 2 x) + 2 (10)}{6} = 0$

Step 1.4.4.3

Factor $2$ out of $2 (- 2 x) + 2 (10)$ .

$\frac{2 (- 2 x + 10)}{6} = 0$

Step 1.4.4.4

Cancel the common factors.

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Step 1.4.4.4.1

Factor $2$ out of $6$ .

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

Step 1.4.4.4.2

Cancel the common factor.

$\frac{2 (- 2 x + 10)}{2 \cdot 3} = 0$

Step 1.4.4.4.3

Rewrite the expression.

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

Step 1.4.5

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

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Step 1.4.5.1

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

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

Step 1.4.5.2

Factor $2$ out of $10$ .

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

Step 1.4.5.3

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

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

Step 1.4.6

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

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

Step 1.4.7

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{2 (- (x) - 1 (- 5))}{3} = 0$

Step 1.4.8

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

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

Step 1.4.9

Simplify the expression.

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Step 1.4.9.1

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

$\frac{2 (- 1 (x - 5))}{3} = 0$

Step 1.4.9.2

Move the negative in front of the fraction.

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

Step 2

Set the numerator equal to zero.

$2 (x - 5) = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

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

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Step 3.1.1

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

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

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.

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

Step 3.1.2.1.2

Divide $x - 5$ by $1$ .

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

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $0$ by $2$ .

$x - 5 = 0$

Step 3.2

Add $5$ to both sides of the equation.

$x = 5$