Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{4}{5} x$ .

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Step 1.1.1

Convert $2 \frac{4}{5}$ 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.

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

Step 1.1.1.2

Add $2$ and $\frac{4}{5}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.1.1.2.2

Combine $2$ and $\frac{5}{5}$ .

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

Step 1.1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 4}{5} x = - 1 \frac{1}{4}$

Step 1.1.1.2.4.2

Add $10$ and $4$ .

$\frac{14}{5} x = - 1 \frac{1}{4}$

Step 1.1.2

Combine $\frac{14}{5}$ and $x$ .

$\frac{14 x}{5} = - 1 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

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

$\frac{14 x}{5} = - (1 + \frac{1}{4})$

Step 2.1.2

Add $1$ and $\frac{1}{4}$ .

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Step 2.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{14 x}{5} = - (\frac{4}{4} + \frac{1}{4})$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{14 x}{5} = - \frac{4 + 1}{4}$

Step 2.1.2.3

Add $4$ and $1$ .

$\frac{14 x}{5} = - \frac{5}{4}$

Step 3

Multiply both sides of the equation by $\frac{5}{14}$ .

$\frac{5}{14} \cdot \frac{14 x}{5} = \frac{5}{14} (- \frac{5}{4})$

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 $\frac{5}{14} \cdot \frac{14 x}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{14} \cdot \frac{14 x}{5} = \frac{5}{14} (- \frac{5}{4})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{14} (14 x) = \frac{5}{14} (- \frac{5}{4})$

Step 4.1.1.2

Cancel the common factor of $14$ .

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Step 4.1.1.2.1

Factor $14$ out of $14 x$ .

$\frac{1}{14} (14 (x)) = \frac{5}{14} (- \frac{5}{4})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{14} (14 x) = \frac{5}{14} (- \frac{5}{4})$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{5}{14} (- \frac{5}{4})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{5}{14} (- \frac{5}{4})$ .

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Step 4.2.1.1

Multiply $\frac{5}{14}$ by $\frac{5}{4}$ .

$x = - \frac{5 \cdot 5}{14 \cdot 4}$

Step 4.2.1.2

Multiply $5$ by $5$ .

$x = - \frac{25}{14 \cdot 4}$

Step 4.2.1.3

Multiply $14$ by $4$ .

$x = - \frac{25}{56}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{25}{56}$

Decimal Form:

$x = - 0.44642857 \dots$