Absolute value equations/inequalities

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

-|−2r − 1| = 11

• {-6,5}
• {5,-6}
• -6
• No Solution

|−4 + 5x| = 16

• {16/5,12/5}
• {4,-5}
• {-12/5, 4}
• 4

−2|−2r − 4| = -12

• {3,1}
• {-3,-1}
• {-3}
• No Solution

∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12

3| −8x| + 8 = 80

• {-7/3, 7/3}
• {-3,3}
• {11/3,-11/3}
• No Solution

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

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8