Question

Which of the following values are solutions to the inequality minus, 8, minus, 4, x, is greater than, 1, question mark−8−4x>1?
I., minus, 10, II., minus, 1, III., 6
I.−10II.−1III.6
Answer
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III

Answer 1

To solve the inequality \(-8 - 4x > 1\), we start by isolating \(x\):

1. Add 8 to both sides:
\[
-4x > 1 + 8
\]
\[
-4x > 9
\]

2. Divide both sides by -4. Remember, when dividing by a negative number, we need to reverse the inequality sign:
\[
x < \frac{9}{-4}
\]
\[
x < -\frac{9}{4}
\]
\[
x < -2.25
\]

Now we can evaluate the given values:

- I. \( -10 \): This is less than \(-2.25\) (solution).
- II. \( -1 \): This is greater than \(-2.25\) (not a solution).
- III. \( 6 \): This is also greater than \(-2.25\) (not a solution).

The only value that satisfies the inequality is \( -10 \).

So the answer is **I only**.