We need to solve the next inequality:
[tex]-9<4x+3<27[/tex]
Then, we can divide into two inequañities
[tex]-9<4x+3[/tex]
We can rewrite the expression as:
[tex]4x+3>-9[/tex]
Subtract both sides 3
[tex]4x+3-3>-9-3[/tex]
[tex]4x>-12[/tex]
Now, divide both sides by 4:
[tex]\frac{4x}{4}>\frac{-12}{4}[/tex][tex]x<-3[/tex]
Also, the other inequality:
[tex]4x+3<27[/tex]
Subtract both sides by 3
[tex]4x+3-3<27-3[/tex][tex]4x<24[/tex]
Then, divide both sides by 4:
[tex]\frac{4x}{4}<\frac{24}{4}[/tex][tex]x<6[/tex]
Therefore, we have the next inequalities for x:
[tex]x>-3[/tex]
and
[tex]x>6[/tex]
Hence, the answer for x is:
[tex]-3
