Question

What is the solution of the inequality x^2-9x+18 less then or equal to zero? Graph solution.

Answer 1

`3\le x\le6`

Step-by-step explanation

The given inequality is

`{x}^(2) - 9x + 18 \leqslant 0`

This is the same as

`(x - 3)(x - 6) \leqslant 0`

The corresponding equation is

`(x - 3)(x - 6)= 0`

By the zero product principle,

`x = 3 \: or \: x = 6`

We now plot the boundaries and test for the region that satisfies the inequality.

See attachment.

From the graph the solution is

`3\le x\le6`