Solving Inequalities Absolute Value Equations and Inequalities

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.

Tags

CCSS.6.NS.C.7C

Solve the absolute value equation. 

• {7}
• {-7, 7}
• {0, 7}
• No Solution

What absolute value inequality does this graph represent?

• |x| < 2

• |x| > 2

• |x| < 2

• |x| > 2

True or False: Is x = 4 a solution to |x + 5| = -9

• True
• False

Solve for x
l 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

What is the first step? 

• Get absolute value alone by subtracting 5 from both sides
• Get absolute value alone by dividing by 5 on both sides
• Split into two equations

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

| x + 1 | ≥ 3

• No Solution
• All Real Numbers
• x ≤ -4  or  x ≥ 2
• -4 ≤ x ≤ 2

| x + 3 | ≤ 2

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5