Algebra Examples

$\frac{3 x - 6}{7} - \frac{3 x + 3}{10} = \frac{9}{70}$

Step 1

Simplify $\frac{3 x - 6}{7} - \frac{3 x + 3}{10}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $3$ out of $3 x - 6$ .

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Step 1.1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{7} - \frac{3 x + 3}{10} = \frac{9}{70}$

Step 1.1.1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{7} - \frac{3 x + 3}{10} = \frac{9}{70}$

Step 1.1.1.3

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

$\frac{3 (x - 2)}{7} - \frac{3 x + 3}{10} = \frac{9}{70}$

Step 1.1.2

Factor $3$ out of $3 x + 3$ .

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Step 1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{3 (x - 2)}{7} - \frac{3 (x) + 3}{10} = \frac{9}{70}$

Step 1.1.2.2

Factor $3$ out of $3$ .

$\frac{3 (x - 2)}{7} - \frac{3 (x) + 3 (1)}{10} = \frac{9}{70}$

Step 1.1.2.3

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

$\frac{3 (x - 2)}{7} - \frac{3 (x + 1)}{10} = \frac{9}{70}$

Step 1.2

To write $\frac{3 (x - 2)}{7}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{3 (x - 2)}{7} \cdot \frac{10}{10} - \frac{3 (x + 1)}{10} = \frac{9}{70}$

Step 1.3

To write $- \frac{3 (x + 1)}{10}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 (x - 2)}{7} \cdot \frac{10}{10} - \frac{3 (x + 1)}{10} \cdot \frac{7}{7} = \frac{9}{70}$

Step 1.4

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 (x - 2)}{7}$ by $\frac{10}{10}$ .

$\frac{3 (x - 2) \cdot 10}{7 \cdot 10} - \frac{3 (x + 1)}{10} \cdot \frac{7}{7} = \frac{9}{70}$

Step 1.4.2

Multiply $7$ by $10$ .

$\frac{3 (x - 2) \cdot 10}{70} - \frac{3 (x + 1)}{10} \cdot \frac{7}{7} = \frac{9}{70}$

Step 1.4.3

Multiply $\frac{3 (x + 1)}{10}$ by $\frac{7}{7}$ .

$\frac{3 (x - 2) \cdot 10}{70} - \frac{3 (x + 1) \cdot 7}{10 \cdot 7} = \frac{9}{70}$

Step 1.4.4

Multiply $10$ by $7$ .

$\frac{3 (x - 2) \cdot 10}{70} - \frac{3 (x + 1) \cdot 7}{70} = \frac{9}{70}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 (x - 2) \cdot 10 - 3 (x + 1) \cdot 7}{70} = \frac{9}{70}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $3$ out of $3 (x - 2) \cdot 10 - 3 (x + 1) \cdot 7$ .

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Step 1.6.1.1

Factor $3$ out of $3 (x - 2) \cdot 10$ .

$\frac{3 ((x - 2) \cdot 10) - 3 (x + 1) \cdot 7}{70} = \frac{9}{70}$

Step 1.6.1.2

Factor $3$ out of $- 3 (x + 1) \cdot 7$ .

$\frac{3 ((x - 2) \cdot 10) + 3 (- (x + 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.1.3

Factor $3$ out of $3 ((x - 2) \cdot 10) + 3 (- (x + 1) \cdot 7)$ .

$\frac{3 ((x - 2) \cdot 10 - (x + 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.2

Apply the distributive property.

$\frac{3 (x \cdot 10 - 2 \cdot 10 - (x + 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.3

Move $10$ to the left of $x$ .

$\frac{3 (10 \cdot x - 2 \cdot 10 - (x + 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.4

Multiply $- 2$ by $10$ .

$\frac{3 (10 \cdot x - 20 - (x + 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.5

Apply the distributive property.

$\frac{3 (10 x - 20 + (- x - 1 \cdot 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.6

Multiply $- 1$ by $1$ .

$\frac{3 (10 x - 20 + (- x - 1) \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.7

Apply the distributive property.

$\frac{3 (10 x - 20 - x \cdot 7 - 1 \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.8

Multiply $7$ by $- 1$ .

$\frac{3 (10 x - 20 - 7 x - 1 \cdot 7)}{70} = \frac{9}{70}$

Step 1.6.9

Multiply $- 1$ by $7$ .

$\frac{3 (10 x - 20 - 7 x - 7)}{70} = \frac{9}{70}$

Step 1.6.10

Subtract $7 x$ from $10 x$ .

$\frac{3 (3 x - 20 - 7)}{70} = \frac{9}{70}$

Step 1.6.11

Subtract $7$ from $- 20$ .

$\frac{3 (3 x - 27)}{70} = \frac{9}{70}$

Step 1.6.12

Factor $3$ out of $3 x - 27$ .

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Step 1.6.12.1

Factor $3$ out of $3 x$ .

$\frac{3 (3 (x) - 27)}{70} = \frac{9}{70}$

Step 1.6.12.2

Factor $3$ out of $- 27$ .

$\frac{3 (3 x + 3 \cdot - 9)}{70} = \frac{9}{70}$

Step 1.6.12.3

Factor $3$ out of $3 x + 3 \cdot - 9$ .

$\frac{3 (3 (x - 9))}{70} = \frac{9}{70}$

$\frac{3 \cdot 3 (x - 9)}{70} = \frac{9}{70}$

Step 1.6.13

Multiply $3$ by $3$ .

$\frac{9 (x - 9)}{70} = \frac{9}{70}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$9 (x - 9) = 9$

Step 3

Divide each term in $9 (x - 9) = 9$ by $9$ and simplify.

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Step 3.1

Divide each term in $9 (x - 9) = 9$ by $9$ .

$\frac{9 (x - 9)}{9} = \frac{9}{9}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{9 (x - 9)}{9} = \frac{9}{9}$

Step 3.2.1.2

Divide $x - 9$ by $1$ .

$x - 9 = \frac{9}{9}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $9$ by $9$ .

$x - 9 = 1$

Step 4

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

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Step 4.1

Add $9$ to both sides of the equation.

$x = 1 + 9$

Step 4.2

Add $1$ and $9$ .

$x = 10$