Solve the Inequality (x^2)-7x+10 <= 0

The first step is to factorise the quadratic leading to the form (x-5)(x-2) <= 0. The next step is to sketch the quadratic equation which means finding intercepts for both the y and x-axis. From inspection the y-intercept is at 10 and the intercepts along the x-axis are 5 and 2. (solving the quadratic for when y=0). From this sketch, the range of x values we are particularly interested in is when the result of the quadratic is negative. The range of values between and including the x-intercepts will satisfy this. Hence, the range of values to satisfy the inequality are 2 <= x < =5.