Algebra Examples

$11 x \frac{1}{7} - 30 x \frac{1}{7} + 21 x \frac{3}{4} - 9 x \frac{3}{4}$

Step 1

Subtract $30 x \frac{1}{7}$ from $11 x \frac{1}{7}$ .

$- 19 x \frac{1}{7} + 21 x \frac{3}{4} - 9 x \frac{3}{4}$

Step 2

Subtract $9 x \frac{3}{4}$ from $21 x \frac{3}{4}$ .

$- 19 x \frac{1}{7} + 12 x \frac{3}{4}$

Step 3

Factor $x$ out of $- 19 x \frac{1}{7} + 12 x \frac{3}{4}$ .

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Step 3.1

Factor $x$ out of $- 19 x \frac{1}{7}$ .

$x (- 19 (\frac{1}{7})) + 12 x \frac{3}{4}$

Step 3.2

Factor $x$ out of $12 x \frac{3}{4}$ .

$x (- 19 (\frac{1}{7})) + x (12 (\frac{3}{4}))$

Step 3.3

Factor $x$ out of $x (- 19 (\frac{1}{7})) + x (12 (\frac{3}{4}))$ .

$x (- 19 (\frac{1}{7}) + 12 (\frac{3}{4}))$

Step 4

Combine $- 19$ and $\frac{1}{7}$ .

$x (\frac{- 19}{7} + 12 (\frac{3}{4}))$

Step 5

Move the negative in front of the fraction.

$x (- \frac{19}{7} + 12 (\frac{3}{4}))$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Factor $4$ out of $12$ .

$x (- \frac{19}{7} + 4 (3) \frac{3}{4})$

Step 6.2

Cancel the common factor.

$x (- \frac{19}{7} + 4 \cdot 3 \frac{3}{4})$

Step 6.3

Rewrite the expression.

$x (- \frac{19}{7} + 3 \cdot 3)$

Step 7

Multiply $3$ by $3$ .

$x (- \frac{19}{7} + 9)$

Step 8

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x (- \frac{19}{7} + 9 \cdot \frac{7}{7})$

Step 9

Combine $9$ and $\frac{7}{7}$ .

$x (- \frac{19}{7} + \frac{9 \cdot 7}{7})$

Step 10

Combine the numerators over the common denominator.

$x \frac{- 19 + 9 \cdot 7}{7}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $9$ by $7$ .

$x \frac{- 19 + 63}{7}$

Step 11.2

Add $- 19$ and $63$ .

$x \frac{44}{7}$