Question

Solve: 4 - |3x + 1| < 2

Answer 1

Hey Ryan!\[\large\rm 4-|3x+1|<2\]Start by subtracting 4 from each side,\[\large\rm -|3x+1|<2-4\]\[\large\rm -|3x+1|<-2\]

Answer 2

Next, multiply each side by -1.
Do you remember what happens when you multiply or divide a negative across an inequality?

Answer 3

4−|3x+1|<2
−|3x+1|+4<2
Step 1: Add -4 to both sides.
−|3x+1|+4+−4<2+−4
−|3x+1|<−2
Step 2: Divide both sides by -1.
−|3x+1|
−1
<
−2
−1
|3x+1|>2
Step 3: Solve Absolute Value.
|3x+1|>2
We know either3x+1>2or3x+1<−2
3x+1>2(Possibility 1)
3x+1−1>2−1(Subtract 1 from both sides)
3x>1
3x
3
>
1
3
(Divide both sides by 3)
x>
1
3
3x+1<−2(Possibility 2)
3x+1−1<−2−1(Subtract 1 from both sides)
3x<−3
3x
3
<
−3
3
(Divide both sides by 3)
x<−1
Answer:
x>
1
3
or x<−1