Solve the absolute value inequality: |x + 12| + 5 < 27 Isolate the absolute value by subtracting 5 from both sides. Sepárate into a compound inequality

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 BSolve 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,∞)thereforeThe solution of the compound inequality is(-34,∞)∩ (-∞,10)=(-34,10)