ANSWER
[tex]3\le x\le6[/tex]
EXPLANATION
The given inequality is
[tex] {x}^{2} - 9x + 18 \leqslant 0[/tex]
This is the same as
[tex](x - 3)(x - 6) \leqslant 0[/tex]
The corresponding equation is
[tex](x - 3)(x - 6)= 0[/tex]
By the zero product principle,
[tex]x = 3 \: or \: x = 6[/tex]
We now plot the boundaries and test for the region that satisfies the inequality.
See attachment.
From the graph the solution is
[tex]3\le x\le6[/tex]
