PLEASE PUT CORRECT ANSWER FOR E D G E N U I T Y FOR A PRIZE
Which inequalities would have an open circle when graphed? Check all that apply.
t Less-than-or-equal-to 25
-2.5 Less-than-or-equal-to m
x > 5.4
1/2 < x
x > 0

Isolate the absolute value expression on the left side of the inequality.

If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3.

Remove the absolute value bars by setting up a compound inequality. The type of inequality sign in the problem will tell us how to set up the compound inequality.

If your problem has a greater than sign (your problem now says that an absolute value is greater than a number), then set up an "or" compound inequality that looks like this:

(quantity inside absolute value) < -(number on other side)

OR

(quantity inside absolute value) > (number on other side)

The same setup is used for a ³ sign.

If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:

-(number on other side) < (quantity inside absolute value) < (number on other side)

The same setup is used for a £ sign

Solve the inequalities.

This process can be a little confusing at first, so be patient while learning how to do these problems. Let’s look at some examples.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: