Question

-2≤1/2-2x/3≤11/6 find the value of x
if x is a set of N​

Answer 1

Answer:

$\huge\boxed{x\in\{0,\ 1,\ 2,\ 3\}}$

Step-by-step explanation:

$-2\leq\dfrac{1}{2}-\dfrac{2x}{3}\leq\dfrac{11}{6}\qquad|\text{multiply all sides by 6}\\\\(6)(-2)\leq(6)\left(\dfrac{1}{2}\right)-(6)\left(\dfrac{2x}{3}\right)\leq(6)\left(\dfrac{11}{6}\right)\\\\-12\leq3-(2)(2x)\leq11\\\\-12\leq3-4x\leq11\qquad|\text{subtract 3 from all sides}\\\\-15\leq-4x\leq8\qquad|\text{change the signs}\\\\15\geq4x\geq-8\qquad|\text{divide all sides by 4}\\\\\dfrac{15}{4}\geq x\geq-2\\\\3\dfrac{3}{4}\geq x\geq-2\\\\x\in\mathbb{N}\\\\\text{therefore}\\\\x\in\{0,\ 1,\ 2,\ 3\}$