Algebra Examples

$2 \frac{3}{4} x - \frac{5}{6} (x - 8 \frac{2}{5})$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

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

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} x - \frac{5}{6} \cdot (x - 8 \frac{2}{5})$

Step 2

Convert $8 \frac{2}{5}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{4} x - \frac{5}{6} \cdot (x - (8 + \frac{2}{5}))$

Step 2.2

Add $8$ and $\frac{2}{5}$ .

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Step 2.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11}{4} x - \frac{5}{6} \cdot (x - (8 \cdot \frac{5}{5} + \frac{2}{5}))$

Step 2.2.2

Combine $8$ and $\frac{5}{5}$ .

$\frac{11}{4} x - \frac{5}{6} \cdot (x - (\frac{8 \cdot 5}{5} + \frac{2}{5}))$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} x - \frac{5}{6} \cdot (x - \frac{8 \cdot 5 + 2}{5})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $8$ by $5$ .

$\frac{11}{4} x - \frac{5}{6} \cdot (x - \frac{40 + 2}{5})$

Step 2.2.4.2

Add $40$ and $2$ .

$\frac{11}{4} x - \frac{5}{6} \cdot (x - \frac{42}{5})$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{11}{4}$ and $x$ .

$\frac{11 x}{4} - \frac{5}{6} \cdot (x - \frac{42}{5})$

Step 3.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11 x}{4} - \frac{5}{6} \cdot (x \cdot \frac{5}{5} - \frac{42}{5})$

Step 3.3

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

$\frac{11 x}{4} - \frac{5}{6} \cdot (\frac{x \cdot 5}{5} - \frac{42}{5})$

Step 3.4

Combine the numerators over the common denominator.

$\frac{11 x}{4} - \frac{5}{6} \cdot \frac{x \cdot 5 - 42}{5}$

Step 3.5

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

$\frac{11 x}{4} - \frac{5}{6} \cdot \frac{5 x - 42}{5}$

Step 3.6

Cancel the common factor of $5$ .

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Step 3.6.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{11 x}{4} + \frac{- 5}{6} \cdot \frac{5 x - 42}{5}$

Step 3.6.2

Factor $5$ out of $- 5$ .

$\frac{11 x}{4} + \frac{5 (- 1)}{6} \cdot \frac{5 x - 42}{5}$

Step 3.6.3

Cancel the common factor.

$\frac{11 x}{4} + \frac{5 \cdot - 1}{6} \cdot \frac{5 x - 42}{5}$

Step 3.6.4

Rewrite the expression.

$\frac{11 x}{4} + \frac{- 1}{6} \cdot (5 x - 42)$

Step 3.7

Move the negative in front of the fraction.

$\frac{11 x}{4} - \frac{1}{6} \cdot (5 x - 42)$

Step 3.8

Apply the distributive property.

$\frac{11 x}{4} - \frac{1}{6} (5 x) - \frac{1}{6} \cdot - 42$

Step 3.9

Multiply $- \frac{1}{6} (5 x)$ .

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Step 3.9.1

Multiply $5$ by $- 1$ .

$\frac{11 x}{4} - 5 (\frac{1}{6}) x - \frac{1}{6} \cdot - 42$

Step 3.9.2

Combine $- 5$ and $\frac{1}{6}$ .

$\frac{11 x}{4} + \frac{- 5}{6} x - \frac{1}{6} \cdot - 42$

Step 3.9.3

Combine $\frac{- 5}{6}$ and $x$ .

$\frac{11 x}{4} + \frac{- 5 x}{6} - \frac{1}{6} \cdot - 42$

Step 3.10

Cancel the common factor of $6$ .

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Step 3.10.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{11 x}{4} + \frac{- 5 x}{6} + \frac{- 1}{6} \cdot - 42$

Step 3.10.2

Factor $6$ out of $- 42$ .

$\frac{11 x}{4} + \frac{- 5 x}{6} + \frac{- 1}{6} \cdot (6 (- 7))$

Step 3.10.3

Cancel the common factor.

$\frac{11 x}{4} + \frac{- 5 x}{6} + \frac{- 1}{6} \cdot (6 \cdot - 7)$

Step 3.10.4

Rewrite the expression.

$\frac{11 x}{4} + \frac{- 5 x}{6} - 1 \cdot - 7$

Step 3.11

Multiply $- 1$ by $- 7$ .

$\frac{11 x}{4} + \frac{- 5 x}{6} + 7$

Step 3.12

Move the negative in front of the fraction.

$\frac{11 x}{4} - \frac{5 x}{6} + 7$

Step 3.13

To write $7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{11 x}{4} - \frac{5 x}{6} + 7 \cdot \frac{6}{6}$

Step 3.14

Combine $7$ and $\frac{6}{6}$ .

$\frac{11 x}{4} - \frac{5 x}{6} + \frac{7 \cdot 6}{6}$

Step 3.15

Combine the numerators over the common denominator.

$\frac{11 x}{4} + \frac{- 5 x + 7 \cdot 6}{6}$

Step 3.16

Multiply $7$ by $6$ .

$\frac{11 x}{4} + \frac{- 5 x + 42}{6}$

Step 4

To write $\frac{11 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 x}{4} \cdot \frac{3}{3} + \frac{- 5 x + 42}{6}$

Step 5

To write $\frac{- 5 x + 42}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 x}{4} \cdot \frac{3}{3} + \frac{- 5 x + 42}{6} \cdot \frac{2}{2}$

Step 6

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{11 x}{4}$ by $\frac{3}{3}$ .

$\frac{11 x \cdot 3}{4 \cdot 3} + \frac{- 5 x + 42}{6} \cdot \frac{2}{2}$

Step 6.2

Multiply $4$ by $3$ .

$\frac{11 x \cdot 3}{12} + \frac{- 5 x + 42}{6} \cdot \frac{2}{2}$

Step 6.3

Multiply $\frac{- 5 x + 42}{6}$ by $\frac{2}{2}$ .

$\frac{11 x \cdot 3}{12} + \frac{(- 5 x + 42) \cdot 2}{6 \cdot 2}$

Step 6.4

Multiply $6$ by $2$ .

$\frac{11 x \cdot 3}{12} + \frac{(- 5 x + 42) \cdot 2}{12}$

Step 7

Combine the numerators over the common denominator.

$\frac{11 x \cdot 3 + (- 5 x + 42) \cdot 2}{12}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $3$ by $11$ .

$\frac{33 x + (- 5 x + 42) \cdot 2}{12}$

Step 8.2

Apply the distributive property.

$\frac{33 x - 5 x \cdot 2 + 42 \cdot 2}{12}$

Step 8.3

Multiply $2$ by $- 5$ .

$\frac{33 x - 10 x + 42 \cdot 2}{12}$

Step 8.4

Multiply $42$ by $2$ .

$\frac{33 x - 10 x + 84}{12}$

Step 8.5

Subtract $10 x$ from $33 x$ .

$\frac{23 x + 84}{12}$