Precalculus Examples

$\frac{x - 2}{3} + \frac{x + 5}{3} = \frac{1}{3}$

Step 1

Simplify $\frac{x - 2}{3} + \frac{x + 5}{3}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x - 2 + x + 5}{3} = \frac{1}{3}$

Step 1.2

Add $x$ and $x$ .

$\frac{2 x - 2 + 5}{3} = \frac{1}{3}$

Step 1.3

Add $- 2$ and $5$ .

$\frac{2 x + 3}{3} = \frac{1}{3}$

Step 2

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

$2 x + 3 = 1$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$2 x = 1 - 3$

Step 3.2

Subtract $3$ from $1$ .

$2 x = - 2$

Step 4

Divide each term in $2 x = - 2$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 2$ by $2$ .

$x = - 1$