Question

solve the compound inequality. \\(-3x\geq -3\\) and \\(2x + 6>16\\) write the solution in interval notation. if there is no solution, enter \\(\varnothing\\).

Explanation:

Step1: Solve first inequality

Divide both sides by -3 (reverse inequality):
$$-3x \geq -3 \implies x \leq 1$$

Step2: Solve second inequality

Subtract 6, then divide by 2:
$$2x + 6 > 16 \implies 2x > 10 \implies x > 5$$

Step3: Find intersection of solutions

No overlap between $x \leq 1$ and $x > 5$.

Answer:

$\emptyset$