Answer:
The solution of the compound inequality is
(-34,∞)∩ (-∞,10)=(-34,10)
Step-by-step explanation:
we have
[tex]\left|x+12\right|+5<27[/tex]
Subtract 5 both sides
[tex]\left|x+12\right|<27-5[/tex]
[tex]\left|x+12\right|<22[/tex]
Separate into a compound inequality
[tex]x+12 <22[/tex] ------> inequality A
[tex]-(x+12)<22[/tex] ------> inequality B
Solve inequality A
[tex]x+12 <22[/tex]
[tex]x <22-12[/tex]
[tex]x <10[/tex]
The solution is the interval (-∞,10)
Solve inequality B
[tex]-(x+12)<22[/tex]
Multiply by -1 both sides
[tex](x+12)>-22[/tex]
[tex]x>-22-12[/tex]
[tex]x>-34[/tex]
The solution is the interval (-34,∞)
therefore
The solution of the compound inequality is
(-34,∞)∩ (-∞,10)=(-34,10)
Answer:
(-34,∞)∩ (-∞,10)=(-34,10)
Step-by-step explanation:
its the seaperate compound inequality
