Question

which of the following values are solutions to the inequality -10 > 3x - 6?

i. - 10 ii. 5 iii. - 1

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 \(-10 > 3x - 6\)

First, add 6 to both sides of the inequality:
\(-10 + 6 > 3x - 6 + 6\)
\(-4 > 3x\)
Then, divide both sides by 3:
\(\frac{-4}{3} > x\)
So \(x < -\frac{4}{3} \approx -1.333\)

Step2: Check each value

• For I. \(x = -10\): Since \(-10 < -1.333\), \(-10\) satisfies the inequality.
• For II. \(x = 5\): Since \(5 > -1.333\), \(5\) does not satisfy the inequality.
• For III. \(x = -1\): Since \(-1 > -1.333\), \(-1\) does not satisfy the inequality.

Answer:

I only