Compound Inequalities and Absolute Value

3 < 2x + 1 < 7

• 1 < x < 3

• 3 < x < 4

• 3 < x < 3

• 2 < x < 6

26 ≤ 7n + 12 < 33

• 2 ≤ n < 3

• 3.7 ≤ n < 3

• 5.4 ≤ n < 6.4

• 4 ≤ n < 3

|v + 8| − 5 = 2 

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2

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

• -14

• -4

• {-14, -4}

• no solution

• no solution

• 40

• 25

• 15

Solve:  -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -1 < x < 3

• 1 < x < 3

• 1 ≤ x ≤ 3

Solve: 
-4x + 1 ≤ 21 and 5x + 2 < 22

• x > -5 or x ≤ 4

• x ≥ -5 or x < 4

• x > -5 and x ≤ 4

• x ≥ -5 and x < 4

−2|−2r − 4| = -12

• {5,1}

• {-5, -1}

• {-5, 1}

• 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.