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]
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
