Absolute Value Inequalities

Which of the following represents the solution to the inequality 2|5-2x|-3<_15 ?

[-2, 7]

Which compound inequality is equivalent to the absolute value inequality |b|>6?

NOT b > -6 or b < 6

A student found the solution below for the given inequality.Which of the following explains whether the student is correct?

NOT The student is partially correct because only one part of the compound inequality is written correctly. NOT The student is partially correct because the student should have written the statements using "or" instead of "and." NOT the student is correct

On any given day, the number of users, u, that access a certain website can be represented by the inequality . Which of the following represents the range of users that access the website each day?

NOT u>_95or u_<155 NOT 95>_u>_155 NOT u<_95 or u>_155

Amber is solving the inequality |x+6|-12<13 by graphing. Which equations should Amber graph?

NOT y1=|x+6|,y2=13 NOT y1=x+6,y2=13

Contessa is solving an absolute value inequality. She writes the compound inequality as her first step. Which inequality is Contessa solving?

|8-3q|<_7

Aaron solved an inequality and then graphed the solution as shown below. Which inequality did Aaron solve?

|x+2|<3

Which inequality is equivalent to|x-4|<9 ?

-9 < x - 4 < 9

What is another way to write the absolute value inequality ?

NOT -12<_p or p<_12 Correct -12<_p<_12

Which compound inequality can be used to solve the inequality ?

NOT -7>3x+2>7 NOT -7<3x+2>7 NOT 3x + 2 > -7 or 3x + 2 > 7

Which compound inequality is equivalent to for all real numbers a, b, and c, where ?

NOT -c<ax-b>c NOT -c>ax-b>c NOT ax-b>-c or ax-b>c

The solution to an absolute value inequality is shown on the graph below.What is another way to show the solution?

(-3, 2)

What is the solution to the inequality |x-4|<3?

1<x<7

A cyclist rides at an average speed of 31 miles per hour. The cyclist's speed, s, can differ from the average by as much as 8 miles per hour. The absolute value inequality represents this situation. If the compound inequality and also represents this situation, what is the value of x in the compound inequality?

NOT -8 or 8 Correct 8

A student showed the steps below while solving the inequality by graphing. Step 1:Write a system of equations: Step 2:Graph the two equations:Step 3:Identify the values of x for which :x = 3 or x = 5Step 4:Write the solution in interval notation:What is the first step in which the student made an error?

NOT Step 2, because the student should have graphed the inequalities Correct Step 3, because the values for x for which also include values between 3 and 5