Pre-Algebra Examples

$- 6 x = 2 \frac{3}{4}$

Step 1

Simplify the right side.

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Step 1.1

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

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Step 1.1.1

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

$- 6 x = 2 + \frac{3}{4}$

Step 1.1.2

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

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Step 1.1.2.1

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

$- 6 x = 2 \cdot \frac{4}{4} + \frac{3}{4}$

Step 1.1.2.2

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

$- 6 x = \frac{2 \cdot 4}{4} + \frac{3}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$- 6 x = \frac{2 \cdot 4 + 3}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$- 6 x = \frac{8 + 3}{4}$

Step 1.1.2.4.2

Add $8$ and $3$ .

$- 6 x = \frac{11}{4}$

Step 2

Divide each term in $- 6 x = \frac{11}{4}$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 x = \frac{11}{4}$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{\frac{11}{4}}{- 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{\frac{11}{4}}{- 6}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{11}{4}}{- 6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{11}{4} \cdot \frac{1}{- 6}$

Step 2.3.2

Move the negative in front of the fraction.

$x = \frac{11}{4} (- \frac{1}{6})$

Step 2.3.3

Multiply $\frac{11}{4} (- \frac{1}{6})$ .

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Step 2.3.3.1

Multiply $\frac{11}{4}$ by $\frac{1}{6}$ .

$x = - \frac{11}{4 \cdot 6}$

Step 2.3.3.2

Multiply $4$ by $6$ .

$x = - \frac{11}{24}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11}{24}$

Decimal Form:

$x = - 0.458\overline{3}$