Pre-Algebra Examples

$- 2 (t + 4 \frac{2}{3}) = 9 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $- 2 (t + 4 \frac{2}{3})$ .

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Step 1.1.1

Convert $4 \frac{2}{3}$ 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.

$- 2 (t + 4 + \frac{2}{3}) = 9 \frac{1}{2}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$- 2 (t + 4 \cdot \frac{3}{3} + \frac{2}{3}) = 9 \frac{1}{2}$

Step 1.1.1.2.2

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

$- 2 (t + \frac{4 \cdot 3}{3} + \frac{2}{3}) = 9 \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$- 2 (t + \frac{4 \cdot 3 + 2}{3}) = 9 \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $4$ by $3$ .

$- 2 (t + \frac{12 + 2}{3}) = 9 \frac{1}{2}$

Step 1.1.1.2.4.2

Add $12$ and $2$ .

$- 2 (t + \frac{14}{3}) = 9 \frac{1}{2}$

Step 1.1.2

Apply the distributive property.

$- 2 t - 2 (\frac{14}{3}) = 9 \frac{1}{2}$

Step 1.1.3

Multiply $- 2 (\frac{14}{3})$ .

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Step 1.1.3.1

Combine $- 2$ and $\frac{14}{3}$ .

$- 2 t + \frac{- 2 \cdot 14}{3} = 9 \frac{1}{2}$

Step 1.1.3.2

Multiply $- 2$ by $14$ .

$- 2 t + \frac{- 28}{3} = 9 \frac{1}{2}$

Step 1.1.4

Move the negative in front of the fraction.

$- 2 t - \frac{28}{3} = 9 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $9 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

$- 2 t - \frac{28}{3} = 9 + \frac{1}{2}$

Step 2.1.2

Add $9$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 t - \frac{28}{3} = 9 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $9$ and $\frac{2}{2}$ .

$- 2 t - \frac{28}{3} = \frac{9 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- 2 t - \frac{28}{3} = \frac{9 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $9$ by $2$ .

$- 2 t - \frac{28}{3} = \frac{18 + 1}{2}$

Step 2.1.2.4.2

Add $18$ and $1$ .

$- 2 t - \frac{28}{3} = \frac{19}{2}$

Step 3

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

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Step 3.1

Add $\frac{28}{3}$ to both sides of the equation.

$- 2 t = \frac{19}{2} + \frac{28}{3}$

Step 3.2

To write $\frac{19}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 2 t = \frac{19}{2} \cdot \frac{3}{3} + \frac{28}{3}$

Step 3.3

To write $\frac{28}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 t = \frac{19}{2} \cdot \frac{3}{3} + \frac{28}{3} \cdot \frac{2}{2}$

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{19}{2}$ by $\frac{3}{3}$ .

$- 2 t = \frac{19 \cdot 3}{2 \cdot 3} + \frac{28}{3} \cdot \frac{2}{2}$

Step 3.4.2

Multiply $2$ by $3$ .

$- 2 t = \frac{19 \cdot 3}{6} + \frac{28}{3} \cdot \frac{2}{2}$

Step 3.4.3

Multiply $\frac{28}{3}$ by $\frac{2}{2}$ .

$- 2 t = \frac{19 \cdot 3}{6} + \frac{28 \cdot 2}{3 \cdot 2}$

Step 3.4.4

Multiply $3$ by $2$ .

$- 2 t = \frac{19 \cdot 3}{6} + \frac{28 \cdot 2}{6}$

Step 3.5

Combine the numerators over the common denominator.

$- 2 t = \frac{19 \cdot 3 + 28 \cdot 2}{6}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $19$ by $3$ .

$- 2 t = \frac{57 + 28 \cdot 2}{6}$

Step 3.6.2

Multiply $28$ by $2$ .

$- 2 t = \frac{57 + 56}{6}$

Step 3.6.3

Add $57$ and $56$ .

$- 2 t = \frac{113}{6}$

Step 4

Divide each term in $- 2 t = \frac{113}{6}$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 t = \frac{113}{6}$ by $- 2$ .

$\frac{- 2 t}{- 2} = \frac{\frac{113}{6}}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 t}{- 2} = \frac{\frac{113}{6}}{- 2}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{\frac{113}{6}}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$t = \frac{113}{6} \cdot \frac{1}{- 2}$

Step 4.3.2

Move the negative in front of the fraction.

$t = \frac{113}{6} (- \frac{1}{2})$

Step 4.3.3

Multiply $\frac{113}{6} (- \frac{1}{2})$ .

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Step 4.3.3.1

Multiply $\frac{113}{6}$ by $\frac{1}{2}$ .

$t = - \frac{113}{6 \cdot 2}$

Step 4.3.3.2

Multiply $6$ by $2$ .

$t = - \frac{113}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{113}{12}$

Decimal Form:

$t = - 9.41\overline{6}$

Mixed Number Form:

$t = - 9 \frac{5}{12}$