Question

|2x| ≤ x + 3

Answer 1

Let's solve your inequality step-by-step.

|2x|≤x+3

Solve Absolute Value.

|2x|≤x+3

Let's find the critical points of the inequality.

|2x|=x+3

We know either2x=x+3or2x=−(x+3)

2x=x+3(Possibility 1)

2x−x=x+3−x(Subtract x from both sides)

x=3

2x=−(x+3)(Possibility 2)

2x=−x−3(Simplify both sides of the equation)

2x+x=−x−3+x(Add x to both sides)

3x=−3

3x

3

=

−3

3

(Divide both sides by 3)

x=−1

Check possible critical points.

x=3(Works in original equation)

x=−1(Works in original equation)

Critical points:

x=3 or x=−1

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤−1(Doesn't work in original inequality)

−1≤x≤3(Works in original inequality)

x≥3(Doesn't work in original inequality)

Answer:

−1≤x≤3

Answer 2

Answer:

[-1,3]

Step-by-step explanation:

|2x|<x+3

calculate the absolute value

2*|x|<x+3

move < to left

2*|x|-x<3

split into possible cases

2x-x<3, x<0

2*(-x)-x<3, x<0

solve inequalities

[0,3]

[-1,0]

find union

[-1,3]