Question

Which of the following are solutions to the inequality below? Select all that apply.

26 ≤
42
x
X=3x=1x=7x=6

Answer 1

To find the solutions to the inequality \( 26 \leq 42x \), we first solve for \( x \):

1. Start with the inequality:
\[
26 \leq 42x
\]

2. To isolate \( x \), divide both sides by 42:
\[
\frac{26}{42} \leq x
\]

3. Simplifying \( \frac{26}{42} \) gives:
\[
\frac{13}{21} \leq x
\]

This inequality means \( x \) must be greater than or equal to \( \frac{13}{21} \).

Now let's evaluate each of the provided options:

- \( x = 3 \): \( 3 \) is greater than \( \frac{13}{21} \) (approximately \( 0.619 \)). So this is a solution.

- \( x = 1 \): \( 1 \) is greater than \( \frac{13}{21} \). So this is also a solution.

- \( x = 7 \): \( 7 \) is greater than \( \frac{13}{21} \). So this is a solution.

- \( x = 6 \): \( 6 \) is greater than \( \frac{13}{21} \). So this is also a solution.

Thus, all of the provided values are solutions to the inequality. The solutions are:

- \( x = 3 \)
- \( x = 1 \)
- \( x = 7 \)
- \( x = 6 \)

All options are correct.