AP Calc
posted by Anon .
Solve the following absolute value inequalities:
x+1<=x3
I promise I'm not posting my whole homework assignment. These are questions that I skipped and have no clue how to do out of a huge packet.

The key to absolute value problems is to remember the definition of n.
n = n if n >= 0
n = n if n < 0
So, here we have
x+1<=x3
if (x3) >= 0, x3 = x3
Also, since that means x > 3, x+1 >= 0, so x+1 = x+1 and we have
x+1 <= x3
1 < 3
not possible
If (x3) < 0, (that is, x<3) we have
x+1 <= (x3)
Now, if x >= 1, x+1 >= 0, and we have
x+1 <= x+3
2x <= 2
x <= 1
But, we required above that x >= 1, so we get a solution set 1 <= x <= 1
If (x3) < 0 and (x+1) < 0 we have
(x+1) <= (x3)
x1 <= x+3
1 < 3
So x < 1 is also a solution.
Combining the solution sets, we see that
x <= 1 is the complete solution set
To see how this works graphically, visit
http://rechneronline.de/functiongraphs/
and enter
abs(x+1)
abs(x3)
as your two functions, and set the domain for x from 5 to 5, and the range y from 0 to 5
This is an excellent place to try out viewing function graphs to confirm your algebra.
Respond to this Question
Similar Questions

math, help
For the following set, which number has the largest absolute value? 
Algebra Packet (a lot of questions!)
Ok, there a lot of questions from the WHOLE packet I received, so please bear with me.  Factor each polynomial (#6+#11) 6. 2x^2+11x+15 11. 36x^249  The … 
Algebra
Right now we are learning about absolute value inequalities. I have to solve and graph this inequality: Pretend my paranpheses are absolute value signs (x4) + 5 is greater than or equal to 10. I assume I would take 5 away from each … 
FACS  Reading Assignment Help!
I have this reading assignment for Family and Consumer Science. She gave us this packet for notes and to read to answer questions she gave us (that's our reading assignment which she is grading). So we answer the questions and to find … 
Combining Inequalities
Some treasure has been buried at a point(x,y)on the grid, where x and y are whole numbers. Here are three clues to help you to find the treasure: Clue 1:x>2 Clue 2:x+y<8 Clue 3: 2yx>0 
SAT Math
Can I please get some help on these questions: 1. If , find the value of 2 square root of 17x = 2x10, find the value of x/4. 2. If absolute value of 3x+6 < 9, then which of the following is a possible value of x ? 
Algebra
I need help with solving these absolute value inequalities. I have to graph them as well. y< x+2+4 and y>x+5+3 I just don't know what to do without a coefficient in front of the absolute value! 
CHEMISTRY URGENT
Does anyone have a "Chemistry in Context 6th edition" by mcgraw and hill book? 
Inequalities & Absolute value
2x+4<5 53x<9 What values of x are both of the inequalities above true? 
@ Sarah  econ
I deleted your 43(!) questions. Since you didn't post your answers, I assume you wanted someone else to cheat and give you the answers. No way! If you try that again, you'll be banned from posting here! If you want to post three or …