Which of the following values are solutions to the inequality minus, 8, minus, 4, x, is greater than, 1, question mark−8−4x>1?

Question

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.