Precalculus Examples

$\frac{3}{2} x + \frac{π}{2} = π$

Step 1

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + \frac{π}{2} = π$

Step 2

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

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Step 2.1

Subtract $\frac{π}{2}$ from both sides of the equation.

$\frac{3 x}{2} = π - \frac{π}{2}$

Step 2.2

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

$\frac{3 x}{2} = π \cdot \frac{2}{2} - \frac{π}{2}$

Step 2.3

Combine $π$ and $\frac{2}{2}$ .

$\frac{3 x}{2} = \frac{π \cdot 2}{2} - \frac{π}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x}{2} = \frac{π \cdot 2 - π}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $2$ to the left of $π$ .

$\frac{3 x}{2} = \frac{2 \cdot π - π}{2}$

Step 2.5.2

Subtract $π$ from $2 π$ .

$\frac{3 x}{2} = \frac{π}{2}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = π$

Step 4

Divide each term in $3 x = π$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = π$ by $3$ .

$\frac{3 x}{3} = \frac{π}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{π}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{π}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{π}{3}$

Decimal Form:

$x = 1.04719755 \dots$