Question

The solution to an inequality is graphed on the number line. What is another way to represent this solution set? O {x | X 4.5) O x | x2 4.5) 5 -3 -2 -1 0 1 2 3 4 5​

Answer 1

Answer: Choice B  $\{x | \ x \le 4.5\}$

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Explanation:

The endpoint is at 4.5 and this endpoint is a filled in circle. So we'll have "or equal to" as part of the inequality sign. This is because we are including the endpoint as part of the shaded solution region.

The other part of the inequality sign is "less than" because the shading is to the left of the endpoint. Any point in the shaded region is less than 4.5, or it could be equal to 4.5

Put another way: x is either 4.5 or smaller

We write that as $x \le 4.5$ which is read out as "x is less than or equal to 4.5"

Surrounding this in curly braces tells the reader we're dealing with a set of values. The first part "x |" means "x such that"

All together we end up with the answer $\{x| \ x \le 4.5\}$ which translates to "x such that x is less than or equal to 4.5"