Calculus Examples Polynomial and Rational Functions

Solve for x

$3 = 3 + | 2 x |$

Step 1

Rewrite the equation as $3 + | 2 x | = 3$ .

$3 + | 2 x | = 3$

Step 2

Move all terms not containing $| 2 x |$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $3$ from both sides of the equation.

$| 2 x | = 3 - 3$

Step 2.2

Subtract $3$ from $3$ .

$| 2 x | = 0$

Step 3

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

$2 x = \pm 0$

Step 4

Plus or minus $0$ is $0$ .

$2 x = 0$

Step 5

Divide each term in $2 x = 0$ by $2$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $0$ by $2$ .

$x = 0$

Enter YOUR Problem

Polynomial and Rational Functions

More step-by-step Calculus examples from this chapter.

How to Use Step-by-Step Examples

Read the worked problem

Each example starts from a real Calculus problem and shows the rule or formula it relies on.

Follow every step

Work through the solution line by line. Underlined terms open a glossary definition.

Solve your own problem

Enter a similar problem in the Calculus solver to get the answer with steps.

Why use Mathway?

Step-by-step solutions

See how every answer is worked out, not just the result.

Every major math subject

From basic math through calculus, statistics and chemistry.

Accurate results

Answers you can check your homework against.

Trusted by students

A reliable tool for homework and learning.

Solve for x

Polynomial and Rational Functions

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Calculus Help