Question 504157: Graph the solution set and write it in interval notation.
a. |x+4|>=7
b.|7x+5|-4<3
c.3x+3<2x+5 or x-2>3
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Graph the solution set and write it in interval notation.
a. |x+4|>=7
b.|7x+5|-4<3
c.3x+3<2x+5 or x-2>3
**
a.|x+4|≥7
x+4≥7
x≥3
or
x+4≤-7
x≤-11
solution:
number line
<====-11]........[3====>
(-∞,-11] U [3, ∞)
..
b. |7x+5|-4<3
7x+5-4<3
7x<2
x<2/7
and
-7x-5-4<3
-7x<12
divide by -7 and reverse inequality sigh
x>-12/7
solution:
(-12/7, 2/7)
number line
<.......(-12/7===2/7).........>
..
c.3x+3<2x+5 or x-2>3
x<2 or x>5
number line
<====2)........(5====>
solution:
(-∞, 2) U (5, ∞)
..
symbols:
"[" includes number
"(" does not include number
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