Algebra Examples

$5 = \frac{5 (12) q + 3 (20)}{2 (12)}$

Step 1

Rewrite the equation as $\frac{5 (12) q + 3 (20)}{2 (12)} = 5$ .

$\frac{5 (12) q + 3 (20)}{2 (12)} = 5$

Step 2

Cancel the common factor of $5 (12) q + 3 (20)$ and $12$ .

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Step 2.1

Factor $3$ out of $5 (12) q$ .

$\frac{3 (5 \cdot (4) q) + 3 (20)}{2 (12)} = 5$

Step 2.2

Factor $3$ out of $3 (5 \cdot (4) q) + 3 (20)$ .

$\frac{3 (5 \cdot (4) q + 20)}{2 (12)} = 5$

Step 2.3

Cancel the common factors.

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Step 2.3.1

Factor $3$ out of $2 (12)$ .

$\frac{3 (5 \cdot (4) q + 20)}{3 (2 \cdot (4))} = 5$

Step 2.3.2

Cancel the common factor.

$\frac{3 (5 \cdot (4) q + 20)}{3 (2 \cdot (4))} = 5$

Step 2.3.3

Rewrite the expression.

$\frac{5 \cdot (4) q + 20}{2 \cdot (4)} = 5$

Step 3

Multiply both sides by $2 \cdot (4)$ .

$\frac{5 \cdot (4) q + 20}{2 \cdot (4)} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5 \cdot (4) q + 20}{2 \cdot (4)} (2 \cdot (4))$ .

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Step 4.1.1.1

Cancel the common factor of $5 \cdot (4) q + 20$ and $2$ .

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Step 4.1.1.1.1

Factor $2$ out of $5 \cdot (4) q$ .

$\frac{2 (5 \cdot (2) q) + 20}{2 \cdot (4)} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.1.2

Factor $2$ out of $20$ .

$\frac{2 (5 \cdot (2) q) + 2 \cdot 10}{2 \cdot 4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.1.3

Factor $2$ out of $2 (5 \cdot (2) q) + 2 (10)$ .

$\frac{2 (5 \cdot (2) q + 10)}{2 \cdot (4)} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.1.4

Cancel the common factors.

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Step 4.1.1.1.4.1

Factor $2$ out of $2 \cdot (4)$ .

$\frac{2 (5 \cdot (2) q + 10)}{2 (4)} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.1.4.2

Cancel the common factor.

$\frac{2 (5 \cdot (2) q + 10)}{2 \cdot 4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.1.4.3

Rewrite the expression.

$\frac{5 \cdot (2) q + 10}{4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2

Cancel the common factor of $5 \cdot (2) q + 10$ and $4$ .

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Step 4.1.1.2.1

Factor $2$ out of $5 \cdot (2) q$ .

$\frac{2 (5 q) + 10}{4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2.2

Factor $2$ out of $10$ .

$\frac{2 (5 q) + 2 (5)}{4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2.3

Factor $2$ out of $2 (5 q) + 2 (5)$ .

$\frac{2 (5 q + 5)}{4} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2.4

Cancel the common factors.

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Step 4.1.1.2.4.1

Factor $2$ out of $4$ .

$\frac{2 (5 q + 5)}{2 (2)} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2.4.2

Cancel the common factor.

$\frac{2 (5 q + 5)}{2 \cdot 2} (2 \cdot (4)) = 5 (2 \cdot (4))$

Step 4.1.1.2.4.3

Rewrite the expression.

$\frac{5 q + 5}{2} (2 \cdot (4)) = 5 (2 \cdot (4))$

$\frac{5 q + 5}{2} (2 (4)) = 5 (2 \cdot (4))$

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{5 q + 5}{2} (2 \cdot 4) = 5 (2 \cdot (4))$

Step 4.1.1.3.2

Rewrite the expression.

$(5 q + 5) \cdot 4 = 5 (2 \cdot (4))$

Step 4.1.1.4

Apply the distributive property.

$5 q \cdot 4 + 5 \cdot 4 = 5 (2 \cdot (4))$

Step 4.1.1.5

Multiply.

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Step 4.1.1.5.1

Multiply $4$ by $5$ .

$20 q + 5 \cdot 4 = 5 (2 \cdot (4))$

Step 4.1.1.5.2

Multiply $5$ by $4$ .

$20 q + 20 = 5 (2 \cdot (4))$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $5 (2 \cdot (4))$ .

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Step 4.2.1.1

Multiply $2$ by $4$ .

$20 q + 20 = 5 \cdot 8$

Step 4.2.1.2

Multiply $5$ by $8$ .

$20 q + 20 = 40$

Step 5

Solve for $q$ .

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Step 5.1

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

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Step 5.1.1

Subtract $20$ from both sides of the equation.

$20 q = 40 - 20$

Step 5.1.2

Subtract $20$ from $40$ .

$20 q = 20$

Step 5.2

Divide each term in $20 q = 20$ by $20$ and simplify.

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Step 5.2.1

Divide each term in $20 q = 20$ by $20$ .

$\frac{20 q}{20} = \frac{20}{20}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $20$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{20 q}{20} = \frac{20}{20}$

Step 5.2.2.1.2

Divide $q$ by $1$ .

$q = \frac{20}{20}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $20$ by $20$ .

$q = 1$