we have the inequality
10 – |3x + 2| < 2 |18x + 12|
solve the inequality by using a graphing tool
so
see the attached image
please wait a minute
the solution is the shaded area
using a wolfrang Alpha
the solution in interval notation
(-16/39, ∞) and
(-∞, -12/13)
we have
the inequality
[tex]10-\mleft|3x+2\mright|<2\mleft|18x+12\mright|[/tex]In this problem
[tex]|18x+12|=6|3x+2|[/tex]substitute
[tex]\begin{gathered} 10-|3x+2|<2(6|3x+2|) \\ 10-|3x+2|<12|3x+2| \\ 10<13|3x+2| \\ \text{rewrite} \\ 13|3x+2|\text{ > 10} \end{gathered}[/tex]Find the First solution
[tex]\begin{gathered} 13(3x+2)\text{> 10} \\ 39x+26>10 \\ 39x>-16 \\ x>-\frac{16}{39} \end{gathered}[/tex]the first solution is the interval (-16/39, infinite)
Find the second solution
[tex]\begin{gathered} 13\lbrack-(3x+2)\rbrack\text{> 10} \\ \text{Multiply by -1 both sides} \\ 13(3x+2)\text{ < -10} \\ 39x+26<\text{ -10} \\ 39x\text{ < -36} \\ x<-\text{ }\frac{36}{39} \\ \text{simplify} \\ x<\text{ }-\text{ }\frac{12}{13} \end{gathered}[/tex]the second solution is the interval (-infinite, -12/13)
