Algebra Examples

$- \frac{1}{2} (6 p + 16) = 7$

Step 1

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

$- 2 (- \frac{1}{2} \cdot (6 p + 16)) = - 2 \cdot 7$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- 2 (- \frac{1}{2} \cdot (6 p + 16))$ .

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Step 2.1.1.1

Apply the distributive property.

$- 2 (- \frac{1}{2} (6 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 (\frac{- 1}{2} (6 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.2.2

Factor $2$ out of $6 p$ .

$- 2 (\frac{- 1}{2} (2 (3 p)) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.2.3

Cancel the common factor.

$- 2 (\frac{- 1}{2} (2 (3 p)) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.2.4

Rewrite the expression.

$- 2 (- 1 (3 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.3

Multiply $3$ by $- 1$ .

$- 2 (- 3 p - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 (- 3 p + \frac{- 1}{2} \cdot 16) = - 2 \cdot 7$

Step 2.1.1.4.2

Factor $2$ out of $16$ .

$- 2 (- 3 p + \frac{- 1}{2} \cdot (2 (8))) = - 2 \cdot 7$

Step 2.1.1.4.3

Cancel the common factor.

$- 2 (- 3 p + \frac{- 1}{2} \cdot (2 \cdot 8)) = - 2 \cdot 7$

Step 2.1.1.4.4

Rewrite the expression.

$- 2 (- 3 p - 1 \cdot 8) = - 2 \cdot 7$

Step 2.1.1.5

Multiply $- 1$ by $8$ .

$- 2 (- 3 p - 8) = - 2 \cdot 7$

Step 2.1.1.6

Apply the distributive property.

$- 2 (- 3 p) - 2 \cdot - 8 = - 2 \cdot 7$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 3$ by $- 2$ .

$6 p - 2 \cdot - 8 = - 2 \cdot 7$

Step 2.1.1.7.2

Multiply $- 2$ by $- 8$ .

$6 p + 16 = - 2 \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $7$ .

$6 p + 16 = - 14$

Step 3

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

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Step 3.1

Subtract $16$ from both sides of the equation.

$6 p = - 14 - 16$

Step 3.2

Subtract $16$ from $- 14$ .

$6 p = - 30$

Step 4

Divide each term in $6 p = - 30$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 p = - 30$ by $6$ .

$\frac{6 p}{6} = \frac{- 30}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 p}{6} = \frac{- 30}{6}$

Step 4.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 30}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 30$ by $6$ .

$p = - 5$