Pre-Algebra Examples

$\frac{4}{5} x - 3 \frac{3}{4} \cdot x = 2 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{4}{5} x - 3 \frac{3}{4} \cdot x$ .

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Step 1.1.1

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

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Step 1.1.1.1

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

$\frac{4}{5} x - (3 + \frac{3}{4}) \cdot x = 2 \frac{1}{2}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$\frac{4}{5} x - (3 \cdot \frac{4}{4} + \frac{3}{4}) \cdot x = 2 \frac{1}{2}$

Step 1.1.1.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{4}{5} x - (\frac{3 \cdot 4}{4} + \frac{3}{4}) \cdot x = 2 \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{4}{5} x - \frac{3 \cdot 4 + 3}{4} \cdot x = 2 \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $4$ .

$\frac{4}{5} x - \frac{12 + 3}{4} \cdot x = 2 \frac{1}{2}$

Step 1.1.1.2.4.2

Add $12$ and $3$ .

$\frac{4}{5} x - \frac{15}{4} \cdot x = 2 \frac{1}{2}$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5} - \frac{15}{4} \cdot x = 2 \frac{1}{2}$

Step 1.1.2.2

Combine $x$ and $\frac{15}{4}$ .

$\frac{4 x}{5} - \frac{x \cdot 15}{4} = 2 \frac{1}{2}$

Step 1.1.2.3

Move $15$ to the left of $x$ .

$\frac{4 x}{5} - \frac{15 x}{4} = 2 \frac{1}{2}$

Step 1.1.3

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4 x}{5} \cdot \frac{4}{4} - \frac{15 x}{4} = 2 \frac{1}{2}$

Step 1.1.4

To write $- \frac{15 x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 x}{5} \cdot \frac{4}{4} - \frac{15 x}{4} \cdot \frac{5}{5} = 2 \frac{1}{2}$

Step 1.1.5

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{4 x}{5}$ by $\frac{4}{4}$ .

$\frac{4 x \cdot 4}{5 \cdot 4} - \frac{15 x}{4} \cdot \frac{5}{5} = 2 \frac{1}{2}$

Step 1.1.5.2

Multiply $5$ by $4$ .

$\frac{4 x \cdot 4}{20} - \frac{15 x}{4} \cdot \frac{5}{5} = 2 \frac{1}{2}$

Step 1.1.5.3

Multiply $\frac{15 x}{4}$ by $\frac{5}{5}$ .

$\frac{4 x \cdot 4}{20} - \frac{15 x \cdot 5}{4 \cdot 5} = 2 \frac{1}{2}$

Step 1.1.5.4

Multiply $4$ by $5$ .

$\frac{4 x \cdot 4}{20} - \frac{15 x \cdot 5}{20} = 2 \frac{1}{2}$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{4 x \cdot 4 - 15 x \cdot 5}{20} = 2 \frac{1}{2}$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Factor $x$ out of $4 x \cdot 4 - 15 x \cdot 5$ .

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Step 1.1.7.1.1

Factor $x$ out of $4 x \cdot 4$ .

$\frac{x (4 \cdot 4) - 15 x \cdot 5}{20} = 2 \frac{1}{2}$

Step 1.1.7.1.2

Factor $x$ out of $- 15 x \cdot 5$ .

$\frac{x (4 \cdot 4) + x (- 15 \cdot 5)}{20} = 2 \frac{1}{2}$

Step 1.1.7.1.3

Factor $x$ out of $x (4 \cdot 4) + x (- 15 \cdot 5)$ .

$\frac{x (4 \cdot 4 - 15 \cdot 5)}{20} = 2 \frac{1}{2}$

Step 1.1.7.2

Multiply $4$ by $4$ .

$\frac{x (16 - 15 \cdot 5)}{20} = 2 \frac{1}{2}$

Step 1.1.7.3

Multiply $- 15$ by $5$ .

$\frac{x (16 - 75)}{20} = 2 \frac{1}{2}$

Step 1.1.7.4

Subtract $75$ from $16$ .

$\frac{x \cdot - 59}{20} = 2 \frac{1}{2}$

Step 1.1.8

Simplify the expression.

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Step 1.1.8.1

Move $- 59$ to the left of $x$ .

$\frac{- 59 \cdot x}{20} = 2 \frac{1}{2}$

Step 1.1.8.2

Move the negative in front of the fraction.

$- \frac{59 x}{20} = 2 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

$- \frac{59 x}{20} = 2 + \frac{1}{2}$

Step 2.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 2.1.2.1

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

$- \frac{59 x}{20} = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

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

$- \frac{59 x}{20} = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{59 x}{20} = \frac{2 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $2$ .

$- \frac{59 x}{20} = \frac{4 + 1}{2}$

Step 2.1.2.4.2

Add $4$ and $1$ .

$- \frac{59 x}{20} = \frac{5}{2}$

Step 3

Multiply both sides of the equation by $- \frac{20}{59}$ .

$- \frac{20}{59} (- \frac{59 x}{20}) = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{20}{59} (- \frac{59 x}{20})$ .

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Step 4.1.1.1

Cancel the common factor of $20$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{20}{59}$ into the numerator.

$\frac{- 20}{59} (- \frac{59 x}{20}) = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{59 x}{20}$ into the numerator.

$\frac{- 20}{59} \cdot \frac{- 59 x}{20} = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.1.3

Factor $20$ out of $- 20$ .

$\frac{20 (- 1)}{59} \cdot \frac{- 59 x}{20} = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{20 \cdot - 1}{59} \cdot \frac{- 59 x}{20} = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{59} (- 59 x) = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.2

Cancel the common factor of $59$ .

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Step 4.1.1.2.1

Factor $59$ out of $- 59 x$ .

$\frac{- 1}{59} (59 (- x)) = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{59} (59 (- x)) = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{20}{59} \cdot \frac{5}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{20}{59} \cdot \frac{5}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{20}{59}$ into the numerator.

$x = \frac{- 20}{59} \cdot \frac{5}{2}$

Step 4.2.1.1.2

Factor $2$ out of $- 20$ .

$x = \frac{2 (- 10)}{59} \cdot \frac{5}{2}$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{2 \cdot - 10}{59} \cdot \frac{5}{2}$

Step 4.2.1.1.4

Rewrite the expression.

$x = \frac{- 10}{59} \cdot 5$

Step 4.2.1.2

Combine $\frac{- 10}{59}$ and $5$ .

$x = \frac{- 10 \cdot 5}{59}$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $- 10$ by $5$ .

$x = \frac{- 50}{59}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{50}{59}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{50}{59}$

Decimal Form:

$x = - 0.84745762 \dots$