Algebra Examples

$\frac{1}{14} \cdot (3 x - 2) = \frac{x + 10}{10}$

Step 1

Multiply both sides by $10$ .

$\frac{1}{14} \cdot (3 x - 2) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1}{14} \cdot (3 x - 2) \cdot 10$ .

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Step 2.1.1.1

Apply the distributive property.

$(\frac{1}{14} (3 x) + \frac{1}{14} \cdot - 2) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.2

Multiply $\frac{1}{14} (3 x)$ .

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Step 2.1.1.2.1

Combine $3$ and $\frac{1}{14}$ .

$(\frac{3}{14} x + \frac{1}{14} \cdot - 2) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.2.2

Combine $\frac{3}{14}$ and $x$ .

$(\frac{3 x}{14} + \frac{1}{14} \cdot - 2) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $14$ .

$(\frac{3 x}{14} + \frac{1}{2 (7)} \cdot - 2) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.3.2

Factor $2$ out of $- 2$ .

$(\frac{3 x}{14} + \frac{1}{2 \cdot 7} \cdot (2 \cdot - 1)) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.3.3

Cancel the common factor.

$(\frac{3 x}{14} + \frac{1}{2 \cdot 7} \cdot (2 \cdot - 1)) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.3.4

Rewrite the expression.

$(\frac{3 x}{14} + \frac{1}{7} \cdot - 1) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.4

Combine $\frac{1}{7}$ and $- 1$ .

$(\frac{3 x}{14} + \frac{- 1}{7}) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.5

Move the negative in front of the fraction.

$(\frac{3 x}{14} - \frac{1}{7}) \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.6

Apply the distributive property.

$\frac{3 x}{14} \cdot 10 - \frac{1}{7} \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $14$ .

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

Step 2.1.1.7.2

Factor $2$ out of $10$ .

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

Step 2.1.1.7.3

Cancel the common factor.

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

Step 2.1.1.7.4

Rewrite the expression.

$\frac{3 x}{7} \cdot 5 - \frac{1}{7} \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.8

Combine $\frac{3 x}{7}$ and $5$ .

$\frac{3 x \cdot 5}{7} - \frac{1}{7} \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.9

Multiply $5$ by $3$ .

$\frac{15 x}{7} - \frac{1}{7} \cdot 10 = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.10

Multiply $- \frac{1}{7} \cdot 10$ .

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Step 2.1.1.10.1

Multiply $10$ by $- 1$ .

$\frac{15 x}{7} - 10 (\frac{1}{7}) = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.10.2

Combine $- 10$ and $\frac{1}{7}$ .

$\frac{15 x}{7} + \frac{- 10}{7} = \frac{x + 10}{10} \cdot 10$

Step 2.1.1.11

Move the negative in front of the fraction.

$\frac{15 x}{7} - \frac{10}{7} = \frac{x + 10}{10} \cdot 10$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{15 x}{7} - \frac{10}{7} = \frac{x + 10}{10} \cdot 10$

Step 2.2.1.2

Rewrite the expression.

$\frac{15 x}{7} - \frac{10}{7} = x + 10$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{15 x}{7} - \frac{10}{7} - x = 10$

Step 3.1.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{15 x}{7} - x \cdot \frac{7}{7} - \frac{10}{7} = 10$

Step 3.1.3

Combine $- x$ and $\frac{7}{7}$ .

$\frac{15 x}{7} + \frac{- x \cdot 7}{7} - \frac{10}{7} = 10$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{15 x - x \cdot 7}{7} - \frac{10}{7} = 10$

Step 3.1.5

Combine the numerators over the common denominator.

$\frac{15 x - x \cdot 7 - 10}{7} = 10$

Step 3.1.6

Multiply $7$ by $- 1$ .

$\frac{15 x - 7 x - 10}{7} = 10$

Step 3.1.7

Subtract $7 x$ from $15 x$ .

$\frac{8 x - 10}{7} = 10$

Step 3.1.8

Factor $2$ out of $8 x - 10$ .

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Step 3.1.8.1

Factor $2$ out of $8 x$ .

$\frac{2 (4 x) - 10}{7} = 10$

Step 3.1.8.2

Factor $2$ out of $- 10$ .

$\frac{2 (4 x) + 2 (- 5)}{7} = 10$

Step 3.1.8.3

Factor $2$ out of $2 (4 x) + 2 (- 5)$ .

$\frac{2 (4 x - 5)}{7} = 10$

Step 3.2

Multiply both sides by $7$ .

$\frac{2 (4 x - 5)}{7} \cdot 7 = 10 \cdot 7$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{2 (4 x - 5)}{7} \cdot 7$ .

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Step 3.3.1.1.1

Cancel the common factor of $7$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{2 (4 x - 5)}{7} \cdot 7 = 10 \cdot 7$

Step 3.3.1.1.1.2

Rewrite the expression.

$2 (4 x - 5) = 10 \cdot 7$

Step 3.3.1.1.2

Apply the distributive property.

$2 (4 x) + 2 \cdot - 5 = 10 \cdot 7$

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $4$ by $2$ .

$8 x + 2 \cdot - 5 = 10 \cdot 7$

Step 3.3.1.1.3.2

Multiply $2$ by $- 5$ .

$8 x - 10 = 10 \cdot 7$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $10$ by $7$ .

$8 x - 10 = 70$

Step 3.4

Solve for $x$ .

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Step 3.4.1

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

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Step 3.4.1.1

Add $10$ to both sides of the equation.

$8 x = 70 + 10$

Step 3.4.1.2

Add $70$ and $10$ .

$8 x = 80$

Step 3.4.2

Divide each term in $8 x = 80$ by $8$ and simplify.

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Step 3.4.2.1

Divide each term in $8 x = 80$ by $8$ .

$\frac{8 x}{8} = \frac{80}{8}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Cancel the common factor of $8$ .

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Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{80}{8}$

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{80}{8}$

Step 3.4.2.3

Simplify the right side.

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Step 3.4.2.3.1

Divide $80$ by $8$ .

$x = 10$