Calculus Examples Polynomial and Rational Functions

Solve for x

$| 3 x | + 3 = 2 + 3$

Step 1

Add $2$ and $3$ .

$| 3 x | + 3 = 5$

Step 2

Move all terms not containing $| 3 x |$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

$| 3 x | = 5 - 3$

Step 2.2

Subtract $3$ from $5$ .

$| 3 x | = 2$

Step 3

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 x = \pm 2$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$3 x = 2$

Step 4.2

Divide each term in $3 x = 2$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x = 2$ by $3$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Next, use the negative value of the $\pm$ to find the second solution.

$3 x = - 2$

Step 4.4

Divide each term in $3 x = - 2$ by $3$ and simplify.

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Step 4.4.1

Divide each term in $3 x = - 2$ by $3$ .

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $3$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $x$ by $1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

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

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{2}{3}, - \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}, - \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}, - 0.\overline{6}$

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