Algebra Examples

$- \frac{1}{2} (t + 3) - 10 = - 6.5$

Step 1

Simplify $- \frac{1}{2} \cdot (t + 3) - 10$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- \frac{1}{2} t - \frac{1}{2} \cdot 3 - 10 = - 6.5$

Step 1.1.2

Combine $t$ and $\frac{1}{2}$ .

$- \frac{t}{2} - \frac{1}{2} \cdot 3 - 10 = - 6.5$

Step 1.1.3

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

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Step 1.1.3.1

Multiply $3$ by $- 1$ .

$- \frac{t}{2} - 3 (\frac{1}{2}) - 10 = - 6.5$

Step 1.1.3.2

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

$- \frac{t}{2} + \frac{- 3}{2} - 10 = - 6.5$

Step 1.1.4

Move the negative in front of the fraction.

$- \frac{t}{2} - \frac{3}{2} - 10 = - 6.5$

Step 1.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{t}{2} - \frac{3}{2} - 10 \cdot \frac{2}{2} = - 6.5$

Step 1.3

Combine $- 10$ and $\frac{2}{2}$ .

$- \frac{t}{2} - \frac{3}{2} + \frac{- 10 \cdot 2}{2} = - 6.5$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{t}{2} + \frac{- 3 - 10 \cdot 2}{2} = - 6.5$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 10$ by $2$ .

$- \frac{t}{2} + \frac{- 3 - 20}{2} = - 6.5$

Step 1.5.2

Subtract $20$ from $- 3$ .

$- \frac{t}{2} + \frac{- 23}{2} = - 6.5$

Step 1.6

Move the negative in front of the fraction.

$- \frac{t}{2} - \frac{23}{2} = - 6.5$

Step 2

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

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Step 2.1

Add $\frac{23}{2}$ to both sides of the equation.

$- \frac{t}{2} = - 6.5 + \frac{23}{2}$

Step 2.2

To write $- 6.5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{t}{2} = - 6.5 \cdot \frac{2}{2} + \frac{23}{2}$

Step 2.3

Combine $- 6.5$ and $\frac{2}{2}$ .

$- \frac{t}{2} = \frac{- 6.5 \cdot 2}{2} + \frac{23}{2}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{t}{2} = \frac{- 6.5 \cdot 2 + 23}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 6.5$ by $2$ .

$- \frac{t}{2} = \frac{- 13 + 23}{2}$

Step 2.5.2

Add $- 13$ and $23$ .

$- \frac{t}{2} = \frac{10}{2}$

Step 2.6

Divide $10$ by $2$ .

$- \frac{t}{2} = 5$

Step 3

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{t}{2}) = - 2 \cdot 5$

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 $- 2 (- \frac{t}{2})$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{t}{2}$ into the numerator.

$- 2 \frac{- t}{2} = - 2 \cdot 5$

Step 4.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- t}{2} = - 2 \cdot 5$

Step 4.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- t}{2} = - 2 \cdot 5$

Step 4.1.1.1.4

Rewrite the expression.

$- - t = - 2 \cdot 5$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 t = - 2 \cdot 5$

Step 4.1.1.2.2

Multiply $t$ by $1$ .

$t = - 2 \cdot 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 2$ by $5$ .

$t = - 10$