Basic Math Examples

$- 5 = \frac{Q - 20}{- 400} \cdot \frac{5800}{\frac{Q + 20}{2}}$

Step 1

Rewrite the equation as $\frac{Q - 20}{- 400} \cdot \frac{5800}{\frac{Q + 20}{2}} = - 5$ .

$\frac{Q - 20}{- 400} \cdot \frac{5800}{\frac{Q + 20}{2}} = - 5$

Step 2

Factor each term.

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Step 2.1

Multiply $\frac{Q - 20}{- 400}$ by $\frac{5800}{\frac{Q + 20}{2}}$ .

$\frac{(Q - 20) \cdot 5800}{- 400 \frac{Q + 20}{2}} = - 5$

Step 2.2

Reduce the expression $\frac{(Q - 20) \cdot 5800}{- 400 \frac{Q + 20}{2}}$ by cancelling the common factors.

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Step 2.2.1

Factor $200$ out of $(Q - 20) \cdot 5800$ .

$\frac{200 ((Q - 20) \cdot 29)}{- 400 \frac{Q + 20}{2}} = - 5$

Step 2.2.2

Factor $200$ out of $- 400 \frac{Q + 20}{2}$ .

$\frac{200 ((Q - 20) \cdot 29)}{200 (- 2 \frac{Q + 20}{2})} = - 5$

Step 2.2.3

Cancel the common factor.

$\frac{200 ((Q - 20) \cdot 29)}{200 (- 2 \frac{Q + 20}{2})} = - 5$

Step 2.2.4

Rewrite the expression.

$\frac{(Q - 20) \cdot 29}{- 2 \frac{Q + 20}{2}} = - 5$

Step 2.3

Combine $- 2$ and $\frac{Q + 20}{2}$ .

$\frac{(Q - 20) \cdot 29}{\frac{- 2 (Q + 20)}{2}} = - 5$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$\frac{- 2 (Q + 20)}{2}, 1$

Step 3.2

Simplify each term.

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Step 3.2.1

Remove parentheses.

$\frac{- 2 (Q + 20)}{2}, 1$

Step 3.2.2

Reduce the expression $\frac{- 2 (Q + 20)}{2}$ by cancelling the common factors.

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Step 3.2.2.1

Factor $2$ out of $- 2 (Q + 20)$ .

$\frac{2 (- (Q + 20))}{2}, 1$

Step 3.2.2.2

Factor $2$ out of $2$ .

$\frac{2 (- (Q + 20))}{2 (1)}, 1$

Step 3.2.2.3

Cancel the common factor.

$\frac{2 (- (Q + 20))}{2 \cdot 1}, 1$

Step 3.2.2.4

Rewrite the expression.

$\frac{- (Q + 20)}{1}, 1$

Step 3.2.3

Divide $- (Q + 20)$ by $1$ .

$- (Q + 20), 1$

Step 3.3

The LCM of one and any expression is the expression.

$- (Q + 20)$

Step 4

Multiply each term in $\frac{(Q - 20) \cdot 29}{\frac{- 2 (Q + 20)}{2}} = - 5$ by $- (Q + 20)$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{(Q - 20) \cdot 29}{\frac{- 2 (Q + 20)}{2}} = - 5$ by $- (Q + 20)$ .

$\frac{(Q - 20) \cdot 29}{\frac{- 2 (Q + 20)}{2}} (- (Q + 20)) = - 5 (- (Q + 20))$

Step 4.2

Simplify the left side.

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Step 4.2.1

Rewrite using the commutative property of multiplication.

$- \frac{(Q - 20) \cdot 29}{\frac{- 2 (Q + 20)}{2}} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.2

Cancel the common factor of $- 2$ and $2$ .

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Step 4.2.2.1

Factor $2$ out of $- 2 (Q + 20)$ .

$- \frac{(Q - 20) \cdot 29}{\frac{2 (- (Q + 20))}{2}} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.2.2

Cancel the common factors.

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Step 4.2.2.2.1

Factor $2$ out of $2$ .

$- \frac{(Q - 20) \cdot 29}{\frac{2 (- (Q + 20))}{2 (1)}} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.2.2.2

Cancel the common factor.

$- \frac{(Q - 20) \cdot 29}{\frac{2 (- (Q + 20))}{2 \cdot 1}} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.2.2.3

Rewrite the expression.

$- \frac{(Q - 20) \cdot 29}{\frac{- (Q + 20)}{1}} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.2.2.4

Divide $- (Q + 20)$ by $1$ .

$- \frac{(Q - 20) \cdot 29}{- (Q + 20)} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.3

Cancel the common factor of $Q + 20$ .

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Step 4.2.3.1

Move the leading negative in $- \frac{(Q - 20) \cdot 29}{- (Q + 20)}$ into the numerator.

$\frac{- (Q - 20) \cdot 29}{- (Q + 20)} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.3.2

Factor $Q + 20$ out of $- (Q + 20)$ .

$\frac{- (Q - 20) \cdot 29}{(Q + 20) \cdot - 1} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.3.3

Cancel the common factor.

$\frac{- (Q - 20) \cdot 29}{(Q + 20) \cdot - 1} (Q + 20) = - 5 (- (Q + 20))$

Step 4.2.3.4

Rewrite the expression.

$\frac{- (Q - 20) \cdot 29}{- 1} = - 5 (- (Q + 20))$

Step 4.2.4

Dividing two negative values results in a positive value.

$\frac{(Q - 20) \cdot 29}{1} = - 5 (- (Q + 20))$

Step 4.2.5

Divide $(Q - 20) \cdot 29$ by $1$ .

$(Q - 20) \cdot 29 = - 5 (- (Q + 20))$

Step 4.2.6

Apply the distributive property.

$Q \cdot 29 - 20 \cdot 29 = - 5 (- (Q + 20))$

Step 4.2.7

Simplify the expression.

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Step 4.2.7.1

Move $29$ to the left of $Q$ .

$29 \cdot Q - 20 \cdot 29 = - 5 (- (Q + 20))$

Step 4.2.7.2

Multiply $- 20$ by $29$ .

$29 Q - 580 = - 5 (- (Q + 20))$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$29 Q - 580 = - 5 (- Q - 1 \cdot 20)$

Step 4.3.2

Multiply $- 1$ by $20$ .

$29 Q - 580 = - 5 (- Q - 20)$

Step 4.3.3

Apply the distributive property.

$29 Q - 580 = - 5 (- Q) - 5 \cdot - 20$

Step 4.3.4

Multiply.

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Step 4.3.4.1

Multiply $- 1$ by $- 5$ .

$29 Q - 580 = 5 Q - 5 \cdot - 20$

Step 4.3.4.2

Multiply $- 5$ by $- 20$ .

$29 Q - 580 = 5 Q + 100$

Step 5

Solve the equation.

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Step 5.1

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

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Step 5.1.1

Subtract $5 Q$ from both sides of the equation.

$29 Q - 580 - 5 Q = 100$

Step 5.1.2

Subtract $5 Q$ from $29 Q$ .

$24 Q - 580 = 100$

Step 5.2

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

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Step 5.2.1

Add $580$ to both sides of the equation.

$24 Q = 100 + 580$

Step 5.2.2

Add $100$ and $580$ .

$24 Q = 680$

Step 5.3

Divide each term in $24 Q = 680$ by $24$ and simplify.

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Step 5.3.1

Divide each term in $24 Q = 680$ by $24$ .

$\frac{24 Q}{24} = \frac{680}{24}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $24$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{24 Q}{24} = \frac{680}{24}$

Step 5.3.2.1.2

Divide $Q$ by $1$ .

$Q = \frac{680}{24}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Cancel the common factor of $680$ and $24$ .

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Step 5.3.3.1.1

Factor $8$ out of $680$ .

$Q = \frac{8 (85)}{24}$

Step 5.3.3.1.2

Cancel the common factors.

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Step 5.3.3.1.2.1

Factor $8$ out of $24$ .

$Q = \frac{8 \cdot 85}{8 \cdot 3}$

Step 5.3.3.1.2.2

Cancel the common factor.

$Q = \frac{8 \cdot 85}{8 \cdot 3}$

Step 5.3.3.1.2.3

Rewrite the expression.

$Q = \frac{85}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$Q = \frac{85}{3}$

Decimal Form:

$Q = 28.\overline{3}$

Mixed Number Form:

$Q = 28 \frac{1}{3}$