Find the interval notation of the solution set of the inequality $2x^2-5x+2>0$, then convert it into inequality notation.

Step 1 ：First, we must solve the inequality. We start by finding the roots of the quadratic equation $2x^2-5x+2=0$.

Step 2 ：This can be done using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, where $a=2$, $b=-5$, and $c=2$.

Step 3 ：Substituting the values, we get $x=\frac{5\pm \sqrt{(-5{)}^2-4\ast 2\ast 2}}{2\ast 2}$ which simplifies to $x=\frac{5\pm \sqrt{9}}{4}$. Therefore, the roots of the equation are $x=1$ and $x=2$.

Step 4 ：Since we want to find when the equation is greater than 0, we test the intervals $-\mathrm{\infty },1$, $1,2$, and $2,\mathrm{\infty }$ to determine where the function is positive.

Step 5 ：If we substitute any value less than 1 into the equation, we get a positive result. If we substitute any value between 1 and 2, we get a negative result. If we substitute any value greater than 2, we get a positive result.

Step 6 ：Therefore, the interval notation for the solution is $(-\mathrm{\infty },1)\cup (2,\mathrm{\infty })$.

Step 7 ：To convert this into inequality notation, we can write it as $x<1$ or $x>2$.