Questions: Which set of numbers contains only solutions to the inequality 2-3x>17? x=-5,-3,0,1 x=-12,-9,-8,-5 x=-9,-8,-7,-6 x=-2,-1,0,1

Solution Steps

To determine which set of numbers contains only solutions to the inequality \(2 - 3x > 17\), we need to solve the inequality for \(x\) and then check each set to see if all its elements satisfy the inequality.

1. Solve the inequality \(2 - 3x > 17\) for \(x\).
2. Substitute each number from the given sets into the inequality to check if it holds true.
3. Identify the set where all numbers satisfy the inequality.

We start with the inequality:

\[ 2 - 3x > 17 \]

Subtracting 2 from both sides gives:

\[ -3x > 15 \]

Dividing both sides by -3 (and reversing the inequality) results in:

\[ x < -5 \]

Next, we evaluate each provided set of numbers to see if all elements satisfy the condition \(x < -5\).

1. Set: \([-5, -3, 0, 1]\)

   • \(-5\) is not less than \(-5\) (fails).

2. Set: \([-12, -9, -8, -5]\)

   • \(-12 < -5\) (true)
   • \(-9 < -5\) (true)
   • \(-8 < -5\) (true)
   • \(-5\) is not less than \(-5\) (fails).

3. Set: \([-9, -8, -7, -6]\)

   • \(-9 < -5\) (true)
   • \(-8 < -5\) (true)
   • \(-7 < -5\) (true)
   • \(-6 < -5\) (true).

4. Set: \([-2, -1, 0, 1]\)

   • \(-2 < -5\) (fails).

From the evaluations, the only set where all numbers satisfy \(x < -5\) is:

\([-9, -8, -7, -6]\)

Final Answer