Question

Select two values for `x` that would make `8+2x\le20` true.
10
8
6
4
and explain

Answer 1

To solve the inequality \( 8 + 2x \leq 20 \), we start by isolating \( x \).

1. Subtract 8 from both sides:
\[
2x \leq 20 - 8
\]
\[
2x \leq 12
\]

2. Next, divide both sides by 2:
\[
x \leq 6
\]

This means that any value of \( x \) less than or equal to 6 will satisfy the inequality \( 8 + 2x \leq 20 \).

Now let's evaluate the given options:
- **10**: This value is greater than 6, so it does not satisfy the inequality.
- **8**: This value is also greater than 6, so it does not satisfy the inequality.
- **6**: This value is equal to 6, so it satisfies the inequality.
- **4**: This value is less than 6, so it satisfies the inequality.

Thus, two values from the options that satisfy the inequality \( 8 + 2x \leq 20 \) are **6** and **4**.

To explain further:
- For \( x = 6 \):
\[
8 + 2(6) = 8 + 12 = 20 \quad \text{(which is equal to 20, satisfying the inequality)}
\]

- For \( x = 4 \):
\[
8 + 2(4) = 8 + 8 = 16 \quad \text{(which is less than 20, satisfying the inequality)}
\]

In conclusion, both \( x = 6 \) and \( x = 4 \) satisfy the inequality \( 8 + 2x \leq 20 \).