Finite Math Examples

$\frac{76}{100} + \frac{88}{100} + \frac{72}{100} + \frac{x}{200} = \frac{x}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{76}{100} + \frac{88}{100} + \frac{72}{100} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{76}{100} + \frac{88}{100} + \frac{72}{100} + \frac{x}{200}) \cdot 4$ .

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Step 2.1.1.1

Combine the numerators over the common denominator.

$(\frac{76 + 88 + 72}{100} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.2

Simplify by adding numbers.

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Step 2.1.1.2.1

Add $76$ and $88$ .

$(\frac{164 + 72}{100} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.2.2

Add $164$ and $72$ .

$(\frac{236}{100} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.3

Cancel the common factor of $236$ and $100$ .

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Step 2.1.1.3.1

Factor $4$ out of $236$ .

$(\frac{4 (59)}{100} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.3.2

Cancel the common factors.

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Step 2.1.1.3.2.1

Factor $4$ out of $100$ .

$(\frac{4 \cdot 59}{4 \cdot 25} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.3.2.2

Cancel the common factor.

$(\frac{4 \cdot 59}{4 \cdot 25} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.3.2.3

Rewrite the expression.

$(\frac{59}{25} + \frac{x}{200}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.4

Apply the distributive property.

$\frac{59}{25} \cdot 4 + \frac{x}{200} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.5

Multiply $\frac{59}{25} \cdot 4$ .

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Step 2.1.1.5.1

Combine $\frac{59}{25}$ and $4$ .

$\frac{59 \cdot 4}{25} + \frac{x}{200} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.5.2

Multiply $59$ by $4$ .

$\frac{236}{25} + \frac{x}{200} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.6

Cancel the common factor of $4$ .

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Step 2.1.1.6.1

Factor $4$ out of $200$ .

$\frac{236}{25} + \frac{x}{4 (50)} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{236}{25} + \frac{x}{4 \cdot 50} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{236}{25} + \frac{x}{50} = \frac{x}{4} \cdot 4$

Step 2.1.1.7

Reorder $\frac{236}{25}$ and $\frac{x}{50}$ .

$\frac{x}{50} + \frac{236}{25} = \frac{x}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x}{50} + \frac{236}{25} = \frac{x}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$\frac{x}{50} + \frac{236}{25} = x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{x}{50} + \frac{236}{25} - x = 0$

Step 3.1.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{50}{50}$ .

$\frac{x}{50} - x \cdot \frac{50}{50} + \frac{236}{25} = 0$

Step 3.1.3

Combine $- x$ and $\frac{50}{50}$ .

$\frac{x}{50} + \frac{- x \cdot 50}{50} + \frac{236}{25} = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 50}{50} + \frac{236}{25} = 0$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $x - x \cdot 50$ .

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Step 3.1.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 50}{50} + \frac{236}{25} = 0$

Step 3.1.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 50}{50} + \frac{236}{25} = 0$

Step 3.1.5.1.1.3

Factor $x$ out of $- x \cdot 50$ .

$\frac{x \cdot 1 + x (- 1 \cdot 50)}{50} + \frac{236}{25} = 0$

Step 3.1.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 50)$ .

$\frac{x (1 - 1 \cdot 50)}{50} + \frac{236}{25} = 0$

Step 3.1.5.1.2

Multiply $- 1$ by $50$ .

$\frac{x (1 - 50)}{50} + \frac{236}{25} = 0$

Step 3.1.5.1.3

Subtract $50$ from $1$ .

$\frac{x \cdot - 49}{50} + \frac{236}{25} = 0$

Step 3.1.5.2

Move $- 49$ to the left of $x$ .

$\frac{- 49 \cdot x}{50} + \frac{236}{25} = 0$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{49 x}{50} + \frac{236}{25} = 0$

Step 3.2

Subtract $\frac{236}{25}$ from both sides of the equation.

$- \frac{49 x}{50} = - \frac{236}{25}$

Step 3.3

Multiply both sides of the equation by $- \frac{50}{49}$ .

$- \frac{50}{49} (- \frac{49 x}{50}) = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $- \frac{50}{49} (- \frac{49 x}{50})$ .

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Step 3.4.1.1.1

Cancel the common factor of $50$ .

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Step 3.4.1.1.1.1

Move the leading negative in $- \frac{50}{49}$ into the numerator.

$\frac{- 50}{49} (- \frac{49 x}{50}) = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.1.2

Move the leading negative in $- \frac{49 x}{50}$ into the numerator.

$\frac{- 50}{49} \cdot \frac{- 49 x}{50} = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.1.3

Factor $50$ out of $- 50$ .

$\frac{50 (- 1)}{49} \cdot \frac{- 49 x}{50} = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.1.4

Cancel the common factor.

$\frac{50 \cdot - 1}{49} \cdot \frac{- 49 x}{50} = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{49} (- 49 x) = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.2

Cancel the common factor of $49$ .

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Step 3.4.1.1.2.1

Factor $49$ out of $- 49 x$ .

$\frac{- 1}{49} (49 (- x)) = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{49} (49 (- x)) = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.3

Multiply.

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Step 3.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{50}{49} (- \frac{236}{25})$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $- \frac{50}{49} (- \frac{236}{25})$ .

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Step 3.4.2.1.1

Cancel the common factor of $25$ .

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Step 3.4.2.1.1.1

Move the leading negative in $- \frac{50}{49}$ into the numerator.

$x = \frac{- 50}{49} (- \frac{236}{25})$

Step 3.4.2.1.1.2

Move the leading negative in $- \frac{236}{25}$ into the numerator.

$x = \frac{- 50}{49} \cdot \frac{- 236}{25}$

Step 3.4.2.1.1.3

Factor $25$ out of $- 50$ .

$x = \frac{25 (- 2)}{49} \cdot \frac{- 236}{25}$

Step 3.4.2.1.1.4

Cancel the common factor.

$x = \frac{25 \cdot - 2}{49} \cdot \frac{- 236}{25}$

Step 3.4.2.1.1.5

Rewrite the expression.

$x = \frac{- 2}{49} \cdot - 236$

Step 3.4.2.1.2

Combine $\frac{- 2}{49}$ and $- 236$ .

$x = \frac{- 2 \cdot - 236}{49}$

Step 3.4.2.1.3

Multiply $- 2$ by $- 236$ .

$x = \frac{472}{49}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{472}{49}$

Decimal Form:

$x = 9.63265306 \dots$

Mixed Number Form:

$x = 9 \frac{31}{49}$