Question

-9 < x <-2. I need help

Answer 1

Answer:

All real numbers larger than -9 and smaller than -2

Step-by-step explanation:

You may be asked to understand what the set of the numbers represented by the variable "x" under the double inequality symbol means.

Recall that the inequality symbol < reads "strictly less than" as you read from left to right, and on the other hand it reads "strictly larger than" if you read from right to left.

Therefore the left part of the inequality that states: -9 < x can be read:

a) from left to right: "negative nine is strictly less than x."

b) from right to left: "x is strictly larger than negative nine."

Similarly you can examine the right hand side of the inequality that states: x < -2:

a) From left to right "x is strictly less than negative two"

b) From right to left: "negative two is strictly larger than x"

To understand what this set of x numbers is, the best thing is to visualize it on the number line. Find on the number line the two given numerical values: -9 and -2 (placed on the left side of the origin zero since they are negative numbers). Mark them on the number line, and visualize all the numbers that are "strictly larger than -9" (which are those located to the right of -9. and also what are the number x that satisfy to be strictly less than -2 (that is to the left of point -2 on the number line.

The x values that satisfy both conditions are those numbers in between -9 and -2 as shown in the attached image highlighted in color green. The parentheses placed in the locations for -9 and -2 on the number line are by convention indicating that the actual values -9 and -2 are NOT included in the set.