Question

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

Answer 1

ANSWER

$3\le x\le6$

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

$3\le x\le6$