which inequanity ? , what is the solution ? and solve

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Which inequality represents this graph?

a. |x + 4| ≤ 1

b. |x - 4| ≥ 1

c. |x - 4| ≤ 1

d. |x + 4| ≤ 1

What is the solution of 2 |3 x - 1| + 2 = 10 ?

a. x = - 11/6 or x = 3/2

b. x = - 1 or x = 5/3

c. x = 3/2 or x = - 1

d. x = 3/2 or x = 5/3

Solve: 13 x - 4 - 9 x + 20 = 0

a. -6

b. 6

c. -4

d. -   12/11

May 7th, 2015

Part 1. The graph is represented by 3 <= x <= 5. Since each inequality has 1 on the right hand side, what can you do to 3 <= x <= 5 to get a 1 on the far right? Subtract 4 from each part of the inequality:

3 - 4 <= x - 4 <= 5 - 4, which means that -1 < x - 4 < 1, which means that |x - 4| < 1.

Part 2. 2 * | 3x - 1 | + 2 = 10. Divide thru by the common factor of 2, getting |3x - 1| + 1 = 5. Now get the absolute value by itself, subtracting 1 on both sides of the inequality,resulting in |3x-1| = 4. This can happen in two ways: a) if 3x-1 = 4 or b) 3x-1 = -4. a) implies that 3x = 5, so that x = 5/3. b) implies that 
3x = -3, so that x = -1. So, the solutions are x = 5./3 and x = -1.

Part 3. 13x - 4 - 9x + 20 = 0 impliies that 13x - 9x - 4 + 20 = 0, which implies that 4x + 16 = 0, which means that 4x = -16, so that x = -4.  

May 8th, 2015

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