Question

Can someone pls solve this with steps and explanations

Answer 1

well, when graphing inequalities, and I take it that's what this is, what we do is, we graph the EQUATION version of it, and then we do the shading.

well, the "equation version" of it will be y = x² - 6x + 11, so we graph that, as you can see in the picture below.

now, what part we shade?

well, we can pick a point above or below it, and do a true/false check, let's use the point you see in the picture, the point (3 , 7), meaning x = 3 and y = 7, let's check if that's true or not.

`y\leqslant x^2-6x+11\qquad \begin{cases} x=3\\ y=7 \end{cases}\implies 7\leqslant (3)^2 -6(3)+11 \\\\\\ 7\leqslant 9-18+11\implies 7\leqslant 2\qquad \textit{is this really true?}`

well, is it really? is 7 actually less than or equals to 2? well, hell no, 7 is much bigger than 2, so that's FALSE, so that area or region is the "false" area, and is the one we "do not shade", so we shade the other area.

now, we could have pick any point below and you'd had seen that it yields a "true" statement, so the true region is the one that gets shaded.

now, the inequality states that "y is less than or equals", so because of the equals part, the line of the graph is a solid line, as you see there in the solid blue line, because the values along the border are also included.