Solving/interpreting linear inequalities in one variable

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

Solve the following inequality:

|3x + 6| ≥ 15

• x ≥ 3 or x ≤ −3

• x ≤ 7 and x ≤ −3

• x ≥ 7 and x ≤ −7

• x ≤ −7 or x ≥ 3

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8

Solve:      
−|−2r − 1| < 11

• r < 5    and    r > -6
• All Real Numbers
• r > 5   or   r < -6
• No Solution

the distance a number is from zero on a number line

• inequality
• absolute value
• negative number
• positive number

Write an absolute value equation given x=-8 and x=21 are boundaries.

• |x-6.5|=14.5

• |x+6.5|=14.5

• no solution

• |x-14.5|=6.5

2|5x|-1>-11

• - 1< x > 1

• x=2 or x=-1

• x=1 and x=-1

• x > -1 or x < 1

|5x|- 2> 28

please answer in Interval Notation

• (-infinity, 6)

• (-6,6)

• (-Infinity, -5)(7, infinity)

• (-infinity, -6)(6,infinity)

Solve.

|4v + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

Solve for x: 4|3x - 5| + 20 > 6

• x < 4/3 or x > 2

• x > 14/3 or x < -4/3

• All real numbers

• No Solution