Respuesta :
We have to solve this inequality.
We divide this inequality at each of the signs and solve for the two boundaries of x.
[tex]\begin{gathered} 3x+1>2x-3 \\ 3x-2x+1>2x-3-2x \\ x+1>-3 \\ x>-3-1 \\ x>-4 \end{gathered}[/tex]We then use the other inequality and solve for x:
[tex]\begin{gathered} 2x-3>x-12 \\ 2x-x-3>x-x-12 \\ x-3>-12 \\ x>-12+3 \\ x>-9 \end{gathered}[/tex]This last result, x > -9, is included in the previous result, as x has to be greater than -4.
We can test the result for x = 0, which should satisfy both equations:
[tex]\begin{gathered} 3\cdot0+1>2\cdot0-3>0-12 \\ 1>-3>-12\longrightarrow\text{True} \end{gathered}[/tex]If x is less or equal than -4, the right side of the inequality won't be satisfied.
If x is less or equal than -9, both sides of the inequality are not satisfied.
Answer:
The interval that is a solution for the compound inequality is x > -4
