Question

Solve
x
2
≤ 6 − x
and sketch the solution on a number line
1. None of these
2. 3 ≤ x ≤ 2
3. −3 ≤ x ≤ 2
4. 0 ≤ x ≤ 1
5. 3 ≤ x ≤ −2
6. −3 ≤ x ≤ 0

Answer 1

*x^2

Answer 2

*x^2≤ 6 − x

Answer 3

Hint: \[x^2+x-6=0\implies(x+3)(x-2)=0.\]

Answer 4

what ? I dont get it

Answer 5

The roots of this polynomial are at \(x=-3\) and \(x=2\). However, the inequality has it that \((x+3)(x-2)\leq0\). Therefore, picking a value inside the range \(-3\leq x\leq2\) will yield a negative number (prove this to convince yourself of it).