Understanding:
The sum of 3 times a number (i'll define it as x) and 4 means [tex]3x+4[/tex] is between -8 and 10 which means the value of 3x+4 is less than 10 and greater than -8. With that said, the inequality for that problem would be [tex]-8<3x+4<10[/tex].
Solving the problem:
Now we know that [tex]-8<3x+4<10[/tex], you can solve the problem by subtracting 4 from each side then dividing by 3.
[tex]-8-4<3x+4-4<10-4\\-12<3x<6\\\frac{-12}{3} <\frac{3x}{3}<\frac{6}{3}\\-4<x<2[/tex]
Final Answer:
[tex]-4<x<2[/tex]
