Question

which of the following values are solutions to the inequality $5 \leq 5 - 6x$?

i. 2 ii. 6 iii. 0

answer
none i only
ii only iii only
i and ii i and iii
ii and iii i, ii and iii

Explanation:

Step1: Solve the inequality \(5 \leq 5 - 6x\)

Subtract 5 from both sides: \(5 - 5 \leq 5 - 5 - 6x\)
Simplify: \(0 \leq -6x\)
Divide both sides by -6 (remember to reverse the inequality sign when dividing by a negative number): \(\frac{0}{-6} \geq \frac{-6x}{-6}\)
Simplify: \(0 \geq x\) or \(x \leq 0\)

Step2: Check each value

• For I. \(x = 2\): \(2 \leq 0\) is false.
• For II. \(x = 6\): \(6 \leq 0\) is false.
• For III. \(x = 0\): \(0 \leq 0\) is true.

Answer:

III only