Question

Which of the following values are solutions to the inequality minus, 2, is less than or equal to, 3, plus, 5, x, question mark−2≤3+5x?
I., 3, II., minus, 1, III., minus, 7
I.3II.−1III.−7
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 \(-2 \leq 3 + 5x\), we will isolate \(x\).

1. Start with the inequality:
\[
-2 \leq 3 + 5x
\]

2. Subtract 3 from both sides:
\[
-2 - 3 \leq 5x
\]
\[
-5 \leq 5x
\]

3. Divide both sides by 5:
\[
-1 \leq x
\]
or equivalently,
\[
x \geq -1
\]

Now that we have found the solution \(x \geq -1\), we can check which of the given values (I. 3, II. -1, III. -7) satisfy this inequality:

- **I. 3**:
\[
3 \geq -1 \quad \text{(True)}
\]

- **II. -1**:
\[
-1 \geq -1 \quad \text{(True)}
\]

- **III. -7**:
\[
-7 \geq -1 \quad \text{(False)}
\]

Thus, the solutions that satisfy the inequality are I (3) and II (-1).

The correct answer is **I and II**.