Algebra Examples

$\frac{2 x}{4 π} + \frac{1 - x}{2} = 0$

Step 1

Simplify $\frac{2 x}{4 π} + \frac{1 - x}{2}$ .

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Step 1.1

Cancel the common factor of $2$ and $4$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{4 π} + \frac{1 - x}{2} = 0$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4 π$ .

$\frac{2 (x)}{2 (2 π)} + \frac{1 - x}{2} = 0$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 x}{2 (2 π)} + \frac{1 - x}{2} = 0$

Step 1.1.2.3

Rewrite the expression.

$\frac{x}{2 π} + \frac{1 - x}{2} = 0$

Step 1.2

To write $\frac{1 - x}{2}$ as a fraction with a common denominator, multiply by $\frac{π}{π}$ .

$\frac{x}{2 π} + \frac{1 - x}{2} \cdot \frac{π}{π} = 0$

Step 1.3

Simplify terms.

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Step 1.3.1

Multiply $\frac{1 - x}{2}$ by $\frac{π}{π}$ .

$\frac{x}{2 π} + \frac{(1 - x) π}{2 π} = 0$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{x + (1 - x) π}{2 π} = 0$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{x + 1 π - x π}{2 π} = 0$

Step 1.4.2

Multiply $π$ by $1$ .

$\frac{x + π - x π}{2 π} = 0$

Step 1.4.3

Reorder terms.

$\frac{- π x + x + π}{2 π} = 0$

Step 1.5

Simplify with factoring out.

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Step 1.5.1

Factor $- 1$ out of $- π x$ .

$\frac{- (π x) + x + π}{2 π} = 0$

Step 1.5.2

Factor $- 1$ out of $x$ .

$\frac{- (π x) - 1 (- x) + π}{2 π} = 0$

Step 1.5.3

Factor $- 1$ out of $- (π x) - 1 (- x)$ .

$\frac{- (π x - x) + π}{2 π} = 0$

Step 1.5.4

Factor $- 1$ out of $π$ .

$\frac{- (π x - x) - 1 (- π)}{2 π} = 0$

Step 1.5.5

Factor $- 1$ out of $- (π x - x) - 1 (- π)$ .

$\frac{- (π x - x - π)}{2 π} = 0$

Step 1.5.6

Simplify the expression.

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Step 1.5.6.1

Rewrite $- (π x - x - π)$ as $- 1 (π x - x - π)$ .

$\frac{- 1 (π x - x - π)}{2 π} = 0$

Step 1.5.6.2

Move the negative in front of the fraction.

$- \frac{π x - x - π}{2 π} = 0$

Step 2

Set the numerator equal to zero.

$π x - x - π = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Add $π$ to both sides of the equation.

$π x - x = π$

Step 3.2

Factor $x$ out of $π x - x$ .

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Step 3.2.1

Factor $x$ out of $π x$ .

$x π - x = π$

Step 3.2.2

Factor $x$ out of $- x$ .

$x π + x \cdot - 1 = π$

Step 3.2.3

Factor $x$ out of $x π + x \cdot - 1$ .

$x (π - 1) = π$

Step 3.3

Divide each term in $x (π - 1) = π$ by $π - 1$ and simplify.

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Step 3.3.1

Divide each term in $x (π - 1) = π$ by $π - 1$ .

$\frac{x (π - 1)}{π - 1} = \frac{π}{π - 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $π - 1$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{x (π - 1)}{π - 1} = \frac{π}{π - 1}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{π}{π - 1}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{π}{π - 1}$

Decimal Form:

$x = 1.46694220 \dots$