Question

which of the following values are solutions to the inequality \\(-9 \geq -9 - 6x\\)?

\\(\quad\\) i. \\(-8\\) \\(\quad\\) ii. \\(2\\) \\(\quad\\) iii. \\(0\\)

answer
\\(\circ\\) none
\\(\circ\\) i only
\\(\circ\\) ii only
\\(\circ\\) iii only
\\(\circ\\) i and ii
\\(\circ\\) i and iii
\\(\circ\\) ii and iii
\\(\circ\\) i, ii and iii

Explanation:

Step1: Solve the inequality

Start with the inequality \(-9 \geq -9 - 6x\). Add \(9\) to both sides: \(-9 + 9 \geq -9 + 9 - 6x\), which simplifies to \(0 \geq -6x\). Then divide both sides by \(-6\) (remember to reverse the inequality sign when dividing by a negative number): \(0 \leq x\) or \(x \geq 0\).

Step2: Check each value

• For I (\(-8\)): \(-8 \geq 0\)? No.
• For II (\(2\)): \(2 \geq 0\)? Yes.
• For III (\(0\)): \(0 \geq 0\)? Yes (since it's "greater than or equal to").

Answer:

II and III