Solving Inequalities Absolute Value Equations and Inequalities

Solve for x.

• x ≥ -3.33 and x ≤ 2

• x > -3.33 and x < 2

• x ≥ -3.33 or x ≤ 2

• x > -3.33 or x < 2

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

4|5x-2|+7>39

• -6/5<x>2

• x=2 or x=-6/5

• x=2 and x=-6/5

• x<-6/5 or x>2

−2|−2r − 4| = -12

• {5,1}

• {-5, -1}

• {-5, 1}

• No Solution

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number

What is the solution of ∣5x-2∣=7x+14?

• x=-1

• x=-1, x=-8

• x=-8

• no solutions

On the interstate for someone to get a ticket for speed, they must be less than 45 mph or greater than 75 mph. What absolute value inequality describes the speeds of those receiving a ticket?

• |x - 120| less than or = 30

• |x - 60| less than or = 15

• |x + 120| greater than or = 30

• |x - 60| greater than or = 15

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.

• Absolute value does not always have to be positive.

• Absolute value is like a clock it has only positive numbers.

• Absolute value is talking about distance, distance is always measured by positive numbers.

An extraneous solution is

• not a concern when solving absolute value equations

• an apparent solution that must be rejected because it does not satisfy the original equation

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2