Algebra Examples

$(x + 5 \frac{1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $(x + 5 \frac{1}{2}) \cdot 0.75$ .

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Step 1.1.1

Convert $5 \frac{1}{2}$ 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.

$(x + 5 + \frac{1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.1.2

Add $5$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

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

$(x + 5 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.1.2.2

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

$(x + \frac{5 \cdot 2}{2} + \frac{1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$(x + \frac{5 \cdot 2 + 1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $5$ by $2$ .

$(x + \frac{10 + 1}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.1.2.4.2

Add $10$ and $1$ .

$(x + \frac{11}{2}) \cdot 0.75 = \frac{5}{8}$

Step 1.1.2

Apply the distributive property.

$x \cdot 0.75 + \frac{11}{2} \cdot 0.75 = \frac{5}{8}$

Step 1.1.3

Move $0.75$ to the left of $x$ .

$0.75 \cdot x + \frac{11}{2} \cdot 0.75 = \frac{5}{8}$

Step 1.1.4

Multiply $\frac{11}{2} \cdot 0.75$ .

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Step 1.1.4.1

Combine $\frac{11}{2}$ and $0.75$ .

$0.75 \cdot x + \frac{11 \cdot 0.75}{2} = \frac{5}{8}$

Step 1.1.4.2

Multiply $11$ by $0.75$ .

$0.75 \cdot x + \frac{8.25}{2} = \frac{5}{8}$

Step 1.1.5

Divide $8.25$ by $2$ .

$0.75 x + 4.125 = \frac{5}{8}$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $4.125$ from both sides of the equation.

$0.75 x = \frac{5}{8} - 4.125$

Step 2.2

To write $- 4.125$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$0.75 x = \frac{5}{8} - 4.125 \cdot \frac{8}{8}$

Step 2.3

Combine $- 4.125$ and $\frac{8}{8}$ .

$0.75 x = \frac{5}{8} + \frac{- 4.125 \cdot 8}{8}$

Step 2.4

Combine the numerators over the common denominator.

$0.75 x = \frac{5 - 4.125 \cdot 8}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4.125$ by $8$ .

$0.75 x = \frac{5 - 33}{8}$

Step 2.5.2

Subtract $33$ from $5$ .

$0.75 x = \frac{- 28}{8}$

Step 2.6

Cancel the common factor of $- 28$ and $8$ .

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Step 2.6.1

Factor $4$ out of $- 28$ .

$0.75 x = \frac{4 (- 7)}{8}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $4$ out of $8$ .

$0.75 x = \frac{4 \cdot - 7}{4 \cdot 2}$

Step 2.6.2.2

Cancel the common factor.

$0.75 x = \frac{4 \cdot - 7}{4 \cdot 2}$

Step 2.6.2.3

Rewrite the expression.

$0.75 x = \frac{- 7}{2}$

Step 2.7

Move the negative in front of the fraction.

$0.75 x = - \frac{7}{2}$

Step 3

Divide each term in $0.75 x = - \frac{7}{2}$ by $0.75$ and simplify.

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Step 3.1

Divide each term in $0.75 x = - \frac{7}{2}$ by $0.75$ .

$\frac{0.75 x}{0.75} = \frac{- \frac{7}{2}}{0.75}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.75$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.75 x}{0.75} = \frac{- \frac{7}{2}}{0.75}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{7}{2}}{0.75}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{7}{2} \cdot \frac{1}{0.75}$

Step 3.3.2

Divide $1$ by $0.75$ .

$x = - \frac{7}{2} \cdot 1.\overline{3}$

Step 3.3.3

Multiply $- \frac{7}{2} \cdot 1.\overline{3}$ .

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Step 3.3.3.1

Multiply $1.\overline{3}$ by $- 1$ .

$x = - 1.\overline{3} (\frac{7}{2})$

Step 3.3.3.2

Combine $- 1.\overline{3}$ and $\frac{7}{2}$ .

$x = \frac{- 1.\overline{3} \cdot 7}{2}$

Step 3.3.3.3

Multiply $- 1.\overline{3}$ by $7$ .

$x = \frac{- 9.\overline{3}}{2}$

Step 3.3.4

Divide $- 9.\overline{3}$ by $2$ .

$x = - 4.\overline{6}$