Algebra Examples

$\frac{5}{6} (12 p - 6) = \frac{- 3}{4} (- 12 p + 24)$

Step 1

Simplify $\frac{5}{6} \cdot (12 p - 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{5}{6} \cdot (12 p - 6) = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.2

Simplify by adding zeros.

$\frac{5}{6} \cdot (12 p - 6) = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.3

Apply the distributive property.

$\frac{5}{6} (12 p) + \frac{5}{6} \cdot - 6 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.4

Cancel the common factor of $6$ .

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Step 1.4.1

Factor $6$ out of $12 p$ .

$\frac{5}{6} (6 (2 p)) + \frac{5}{6} \cdot - 6 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.4.2

Cancel the common factor.

$\frac{5}{6} (6 (2 p)) + \frac{5}{6} \cdot - 6 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.4.3

Rewrite the expression.

$5 (2 p) + \frac{5}{6} \cdot - 6 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.5

Multiply $2$ by $5$ .

$10 p + \frac{5}{6} \cdot - 6 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.6

Cancel the common factor of $6$ .

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Step 1.6.1

Factor $6$ out of $- 6$ .

$10 p + \frac{5}{6} \cdot (6 (- 1)) = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.6.2

Cancel the common factor.

$10 p + \frac{5}{6} \cdot (6 \cdot - 1) = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.6.3

Rewrite the expression.

$10 p + 5 \cdot - 1 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 1.7

Multiply $5$ by $- 1$ .

$10 p - 5 = \frac{- 3}{4} \cdot (- 12 p + 24)$

Step 2

Simplify $\frac{- 3}{4} \cdot (- 12 p + 24)$ .

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Step 2.1

Move the negative in front of the fraction.

$10 p - 5 = - \frac{3}{4} \cdot (- 12 p + 24)$

Step 2.2

Apply the distributive property.

$10 p - 5 = - \frac{3}{4} (- 12 p) - \frac{3}{4} \cdot 24$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$10 p - 5 = \frac{- 3}{4} (- 12 p) - \frac{3}{4} \cdot 24$

Step 2.3.2

Factor $4$ out of $- 12 p$ .

$10 p - 5 = \frac{- 3}{4} (4 (- 3 p)) - \frac{3}{4} \cdot 24$

Step 2.3.3

Cancel the common factor.

$10 p - 5 = \frac{- 3}{4} (4 (- 3 p)) - \frac{3}{4} \cdot 24$

Step 2.3.4

Rewrite the expression.

$10 p - 5 = - 3 (- 3 p) - \frac{3}{4} \cdot 24$

Step 2.4

Multiply $- 3$ by $- 3$ .

$10 p - 5 = 9 p - \frac{3}{4} \cdot 24$

Step 2.5

Cancel the common factor of $4$ .

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Step 2.5.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$10 p - 5 = 9 p + \frac{- 3}{4} \cdot 24$

Step 2.5.2

Factor $4$ out of $24$ .

$10 p - 5 = 9 p + \frac{- 3}{4} \cdot (4 (6))$

Step 2.5.3

Cancel the common factor.

$10 p - 5 = 9 p + \frac{- 3}{4} \cdot (4 \cdot 6)$

Step 2.5.4

Rewrite the expression.

$10 p - 5 = 9 p - 3 \cdot 6$

Step 2.6

Multiply $- 3$ by $6$ .

$10 p - 5 = 9 p - 18$

Step 3

Move all terms containing $p$ to the left side of the equation.

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Step 3.1

Subtract $9 p$ from both sides of the equation.

$10 p - 5 - 9 p = - 18$

Step 3.2

Subtract $9 p$ from $10 p$ .

$p - 5 = - 18$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$p = - 18 + 5$

Step 4.2

Add $- 18$ and $5$ .

$p = - 13$