One Step Absolute Value Inequalities

Which of the following is a property of absolute value inequalities?

• They always have a single solution

• They can have no solution or infinitely many solutions

• They are always represented by a quadratic equation

• They are solved using logarithms

How do you determine the solution set for an absolute value inequality?

• By finding the intersection of two linear equations

• By solving two separate inequalities

• By graphing a parabola

• By using the quadratic formula

What is the solution set for the inequality |3x + 2| < 4?

• -2 < x < 2

• -2 < x < 4/3

• -4/3 < x < 2

• -4/3 < x < 2/3

|x| = 5

• x = 5

• x = 5 or x = -5

• x = -5

• x = 5 or x = 1/5

What is the first step?

• Get the absolute value alone by dividing both sides by 5

• Drop the absolute value bars and add 7 and 5 together

• Get the absolute value alone by subtracting 5 from both sides

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"

Solve for x
l 5x l = 40

• x = 8 and x =-8

• x = 35 and x = -35

• Only x = 8

• No Solution

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4

• x = 5 and x = -5

• Only x = 5

• No Solution

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0

• x = 3 and x = -3

• x = -12 and x = 0

• No Solution

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution