Question

The number line represents the solution to which inequality?

Answer 1

Answer: Choice G
`3\text{x} \le 21`

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Reason:

The inequality for choice G solves to the following shown below.

`3\text{x} \le 21\\\\3\text{x}/3 \le 21/3\\\\\text{x} \le 7\\\\`

In the second step, I divided both sides by 3 to undo the multiplication going on when saying "3x".

Once we arrive at
`\text{x} \le 7`, the graph will have a closed endpoint at 7 and shading to the left. This is to visually describe all values of x that are 7 or smaller. The endpoint is included as part of the solution set.

This shows why choice G is the answer.

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Something like choice F has the inequality
`\text{x}-2 \le 9` solve to
`\text{x} \le 11` after adding 2 to both sides. The graph of
`\text{x} \le 11` involves a closed endpoint at 11 and shading to the left, which doesn't match the given number line graph. This allows us to rule out choice F.

Choices H and J are ruled out for similar reasoning.