Algebra Examples

$x - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1

Simplify $x - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1.1.2

Multiply $\frac{x}{1}$ by $\frac{30}{30}$ .

$\frac{x}{1} \cdot \frac{30}{30} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1.1.3

Multiply $\frac{x}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 30}{30} - \frac{x - 1}{3} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1.1.4

Multiply $\frac{x - 1}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 30}{30} - (\frac{x - 1}{3} \cdot \frac{10}{10}) - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1.1.5

Multiply $\frac{x - 1}{3}$ by $\frac{10}{10}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{2 x - 5}{5} + \frac{x + 8}{6} = 7$

Step 1.1.6

Multiply $\frac{2 x - 5}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - (\frac{2 x - 5}{5} \cdot \frac{6}{6}) + \frac{x + 8}{6} = 7$

Step 1.1.7

Multiply $\frac{2 x - 5}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{x + 8}{6} = 7$

Step 1.1.8

Multiply $\frac{x + 8}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{x + 8}{6} \cdot \frac{5}{5} = 7$

Step 1.1.9

Multiply $\frac{x + 8}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{3 \cdot 10} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Step 1.1.10

Multiply $3$ by $10$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{5 \cdot 6} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Step 1.1.11

Multiply $5$ by $6$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{6 \cdot 5} = 7$

Step 1.1.12

Reorder the factors of $6 \cdot 5$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{5 \cdot 6} = 7$

Step 1.1.13

Multiply $5$ by $6$ .

$\frac{x \cdot 30}{30} - \frac{(x - 1) \cdot 10}{30} - \frac{(2 x - 5) \cdot 6}{30} + \frac{(x + 8) \cdot 5}{30} = 7$

Step 1.2

Combine the numerators over the common denominator.

$\frac{x \cdot 30 - (x - 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3

Simplify each term.

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Step 1.3.1

Move $30$ to the left of $x$ .

$\frac{30 \cdot x - (x - 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.2

Apply the distributive property.

$\frac{30 x + (- x - - 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.3

Multiply $- 1$ by $- 1$ .

$\frac{30 x + (- x + 1) \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.4

Apply the distributive property.

$\frac{30 x - x \cdot 10 + 1 \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.5

Multiply $10$ by $- 1$ .

$\frac{30 x - 10 x + 1 \cdot 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.6

Multiply $10$ by $1$ .

$\frac{30 x - 10 x + 10 - (2 x - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.7

Apply the distributive property.

$\frac{30 x - 10 x + 10 + (- (2 x) - - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.8

Multiply $2$ by $- 1$ .

$\frac{30 x - 10 x + 10 + (- 2 x - - 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.9

Multiply $- 1$ by $- 5$ .

$\frac{30 x - 10 x + 10 + (- 2 x + 5) \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.10

Apply the distributive property.

$\frac{30 x - 10 x + 10 - 2 x \cdot 6 + 5 \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.11

Multiply $6$ by $- 2$ .

$\frac{30 x - 10 x + 10 - 12 x + 5 \cdot 6 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.12

Multiply $5$ by $6$ .

$\frac{30 x - 10 x + 10 - 12 x + 30 + (x + 8) \cdot 5}{30} = 7$

Step 1.3.13

Apply the distributive property.

$\frac{30 x - 10 x + 10 - 12 x + 30 + x \cdot 5 + 8 \cdot 5}{30} = 7$

Step 1.3.14

Move $5$ to the left of $x$ .

$\frac{30 x - 10 x + 10 - 12 x + 30 + 5 \cdot x + 8 \cdot 5}{30} = 7$

Step 1.3.15

Multiply $8$ by $5$ .

$\frac{30 x - 10 x + 10 - 12 x + 30 + 5 x + 40}{30} = 7$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Subtract $10 x$ from $30 x$ .

$\frac{20 x + 10 - 12 x + 30 + 5 x + 40}{30} = 7$

Step 1.4.2

Subtract $12 x$ from $20 x$ .

$\frac{8 x + 10 + 30 + 5 x + 40}{30} = 7$

Step 1.4.3

Add $8 x$ and $5 x$ .

$\frac{13 x + 10 + 30 + 40}{30} = 7$

Step 1.4.4

Simplify by adding numbers.

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Step 1.4.4.1

Add $10$ and $30$ .

$\frac{13 x + 40 + 40}{30} = 7$

Step 1.4.4.2

Add $40$ and $40$ .

$\frac{13 x + 80}{30} = 7$

Step 2

Multiply both sides by $30$ .

$\frac{13 x + 80}{30} \cdot 30 = 7 \cdot 30$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $30$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{13 x + 80}{30} \cdot 30 = 7 \cdot 30$

Step 3.1.1.2

Rewrite the expression.

$13 x + 80 = 7 \cdot 30$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $7$ by $30$ .

$13 x + 80 = 210$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $80$ from both sides of the equation.

$13 x = 210 - 80$

Step 4.1.2

Subtract $80$ from $210$ .

$13 x = 130$

Step 4.2

Divide each term in $13 x = 130$ by $13$ and simplify.

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Step 4.2.1

Divide each term in $13 x = 130$ by $13$ .

$\frac{13 x}{13} = \frac{130}{13}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $13$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{130}{13}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{130}{13}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $130$ by $13$ .

$x = 10$