Let the inequality:
[tex]3\text{ }<\text{ 2x - 3}\leq\text{ 13}[/tex]
1. we add + 3 :
[tex]3\text{ +3}<\text{ 2x }\leq\text{ 13}+3[/tex]
this is equivalent to :
[tex]6<\text{ 2x }\leq\text{ 1}6[/tex]
we resolve for x ( we divide by 2) :
[tex]3<\text{ x }\leq8[/tex]
that is the interval:
[tex](3,\text{ 8}\rbrack[/tex]
on the real line, the interval is:
On the other hand, the inequality:
[tex]-2\text{ }<\frac{3+x}{4}\leq\text{ 3}[/tex]
1. Multiply by 4:
[tex]-8\text{ }<3+x\leq12[/tex]
2. Add -3:
[tex]-11\text{ }that is the interval:
[tex](-11,\text{ 9}\rbrack[/tex]
on the real line, the interval is:
