For this case we have the following inequality:
[tex]-4\leq 2x + 6 <12[/tex]
We want to clear x, for this we start subtracting 6 from each term, that is:
[tex]-4-6\leq 2x + 6-6 <12-6[/tex]
Resolving the operations we have left:
[tex]-10\leq 2x <6[/tex]
We divide by 2 each term:
[tex]-\frac{10}{2}\leq\frac{2x}{2} <\frac{6}{2}[/tex]
Resolving the operations we obtain:
[tex]-5\leq x<3[/tex]
That is: x: [-5,3)
Answer:
[tex]-5\leq x<3[/tex]
