To solve the inequality [tex]\(5m + 1 \leq 4\)[/tex], we need to isolate [tex]\(m\)[/tex] on one side of the inequality. Let's solve this step-by-step.
1. Start with the given inequality:
[tex]\[
5m + 1 \leq 4
\][/tex]
2. Subtract 1 from both sides to isolate the term with [tex]\(m\)[/tex]:
[tex]\[
5m \leq 4 - 1
\][/tex]
This simplifies to:
[tex]\[
5m \leq 3
\][/tex]
3. Divide both sides by 5 to solve for [tex]\(m\)[/tex]:
[tex]\[
m \leq \frac{3}{5}
\][/tex]
This means [tex]\(m\)[/tex] must be less than or equal to [tex]\(\frac{3}{5}\)[/tex] (which is 0.6 in decimal form) to satisfy the inequality.
Now, let's evaluate the given [tex]\(m\)[/tex]-values:
- For [tex]\(m = 0\)[/tex]:
[tex]\[
5(0) + 1 = 1 \leq 4
\][/tex]
This is true since 1 is less than 4, so [tex]\(m = 0\)[/tex] satisfies the inequality.
- For [tex]\(m = 1\)[/tex]:
[tex]\[
5(1) + 1 = 6 \leq 4
\][/tex]
This is false since 6 is greater than 4, so [tex]\(m = 1\)[/tex] does not satisfy the inequality.
- For [tex]\(m = 2\)[/tex]:
[tex]\[
5(2) + 1 = 11 \leq 4
\][/tex]
This is false since 11 is greater than 4, so [tex]\(m = 2\)[/tex] does not satisfy the inequality.
Thus, the [tex]\(m\)[/tex]-values that satisfy the inequality [tex]\(5m + 1 \leq 4\)[/tex] are:
- A) [tex]\(m = 0\)[/tex]
So, the correct answer is:
- A) [tex]\(m = 0\)[/tex]
