which inequanity ? , what is the solution ? and solve

Mathematics
Tutor: None Selected Time limit: 1 Day

https://tcan4424-oakcliff-ccl.gradpoint.com/Resour...

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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 7th, 2015
...
May 7th, 2015
Feb 25th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer