Basic Math Examples

$9 = \frac{- 6 p - (- 3)}{8}$

Step 1

Rewrite the equation as $\frac{- 6 p - (- 3)}{8} = 9$ .

$\frac{- 6 p - (- 3)}{8} = 9$

Step 2

Multiply both sides by $8$ .

$\frac{- 6 p - (- 3)}{8} \cdot 8 = 9 \cdot 8$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{- 6 p - (- 3)}{8} \cdot 8$ .

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Step 3.1.1.1

Simplify the numerator.

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Step 3.1.1.1.1

Multiply $- 1$ by $- 3$ .

$\frac{- 6 p + 3}{8} \cdot 8 = 9 \cdot 8$

Step 3.1.1.1.2

Factor $3$ out of $- 6 p + 3$ .

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Step 3.1.1.1.2.1

Factor $3$ out of $- 6 p$ .

$\frac{3 (- 2 p) + 3}{8} \cdot 8 = 9 \cdot 8$

Step 3.1.1.1.2.2

Factor $3$ out of $3$ .

$\frac{3 (- 2 p) + 3 (1)}{8} \cdot 8 = 9 \cdot 8$

Step 3.1.1.1.2.3

Factor $3$ out of $3 (- 2 p) + 3 (1)$ .

$\frac{3 (- 2 p + 1)}{8} \cdot 8 = 9 \cdot 8$

$\frac{3 (- 2 p + 1)}{8} \cdot 8 = 9 \cdot 8$

$\frac{3 (- 2 p + 1)}{8} \cdot 8 = 9 \cdot 8$

Step 3.1.1.2

Simplify terms.

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Step 3.1.1.2.1

Cancel the common factor of $8$ .

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Step 3.1.1.2.1.1

Cancel the common factor.

$\frac{3 (- 2 p + 1)}{8} \cdot 8 = 9 \cdot 8$

Step 3.1.1.2.1.2

Rewrite the expression.

$3 (- 2 p + 1) = 9 \cdot 8$

$3 (- 2 p + 1) = 9 \cdot 8$

Step 3.1.1.2.2

Apply the distributive property.

$3 (- 2 p) + 3 \cdot 1 = 9 \cdot 8$

Step 3.1.1.2.3

Multiply.

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Step 3.1.1.2.3.1

Multiply $- 2$ by $3$ .

$- 6 p + 3 \cdot 1 = 9 \cdot 8$

Step 3.1.1.2.3.2

Multiply $3$ by $1$ .

$- 6 p + 3 = 9 \cdot 8$

$- 6 p + 3 = 9 \cdot 8$

$- 6 p + 3 = 9 \cdot 8$

$- 6 p + 3 = 9 \cdot 8$

$- 6 p + 3 = 9 \cdot 8$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $9$ by $8$ .

$- 6 p + 3 = 72$

$- 6 p + 3 = 72$

$- 6 p + 3 = 72$

Step 4

Solve for $p$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$- 6 p = 72 - 3$

Step 4.1.2

Subtract $3$ from $72$ .

$- 6 p = 69$

$- 6 p = 69$

Step 4.2

Divide each term in $- 6 p = 69$ by $- 6$ and simplify.

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Step 4.2.1

Divide each term in $- 6 p = 69$ by $- 6$ .

$\frac{- 6 p}{- 6} = \frac{69}{- 6}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 6 p}{- 6} = \frac{69}{- 6}$

Step 4.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{69}{- 6}$

$p = \frac{69}{- 6}$

$p = \frac{69}{- 6}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $69$ and $- 6$ .

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Step 4.2.3.1.1

Factor $3$ out of $69$ .

$p = \frac{3 (23)}{- 6}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $3$ out of $- 6$ .

$p = \frac{3 \cdot 23}{3 \cdot - 2}$

Step 4.2.3.1.2.2

Cancel the common factor.

$p = \frac{3 \cdot 23}{3 \cdot - 2}$

Step 4.2.3.1.2.3

Rewrite the expression.

$p = \frac{23}{- 2}$

$p = \frac{23}{- 2}$

$p = \frac{23}{- 2}$

Step 4.2.3.2

Move the negative in front of the fraction.

$p = - \frac{23}{2}$

$p = - \frac{23}{2}$

$p = - \frac{23}{2}$

$p = - \frac{23}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{23}{2}$

Decimal Form:

$p = - 11.5$

Mixed Number Form:

$p = - 11 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$