Question

Resolva as seguintes inequaçoes:
a) -2 < 3x +1 < 2  
b) 1 menor ou igual x +1 menor ou igual 2x  
c) -3 < 2x +1 < 5 
d) -2 menor ou igual 3x +7 < 4x 

Answer 1

$a)-2-1\ \textless \ 3x +1-1 \ \textless \ 2-1--\ \textgreater \ -3\ \textless \ 3x\ \textless \ 1(:3);-1 \ \textless \ x \ \textless \ \frac{1}{3} ;$ $b)1 \leq x+1 \leq 2x; \left \{ {{x+1 \geq 1} \atop {x+1 \leq 2x}} \right. --\ \textgreater \ \left \{ {{x \geq 1-1} \atop {1 \leq 2x -x}} \right. --\ \textgreater \ \left \{ {{x \geq 0} \atop {x \geq 1}} \right. --\ \textgreater \ x \geq 1;$ $c)-3 \ \textless \ 2x+1 \ \textless \ 5--\ \textgreater \ -3-1 \ \textless \ 2x+1-1\ \textless \ 5-1;-4 \ \textless \ 2x \ \textless \ 4;$$\frac{-4}{2}\ \textless \ \frac{2x}{2} \ \textless \ \frac{4}{2}--\ \textgreater \ -2 \ \textless \ x \ \textless \ 2;$ $d)-2\leq 3x+7 \ \textless \ 4x; \left \{ {{3x+7\geq -2} \atop {3x+7 \ \textless \ 4x}} \right. --\ \textgreater \ \left \{ {{3x \geq -2-7} \atop {7\ \textless \ 4x -3x}} \right.;\left \{ {{3x \geq -9} \atop {x \ \textgreater \ 7}} \right.-\ \textgreater \ x\ \textgreater \ 7$