Soling an inequality using Algebraic method

In summary, the student attempted to solve an inequality by creating columns and using a number line. However, the student made mistakes and was not able to solve the inequality.
  • #1
Plutonium88
174
0

Homework Statement


Solve
|3x-7|-|x-8|>4



The Attempt at a Solution



so i made columns... and using the columns i made a number line..

7/3 on the left as a point, with a column on its left, and 8 with a column on its right and sharing a coumn in the middle with 7/3

so i have..

|3x-7| => (3x-7), X>OREQUAL 7/3
-(3x-7) x<7/3


|x-8| => (x-8) x>or equal 8
-(x-8) x< 8

* i algebraeicly solved 3 different inequalities after this
1. -(3x-7)-[-(x-8)]>4 (this was not crossed out)-- the answer was crossed x<-2
2. -(3x-7) - (x-8)>4 (this WAS CROSSED OUT)
3. (3x-7) - (x-8) >4 (this was not crossed out) - the answered was crossed x>2/3

i understand i am supposed to compare the three inequalities after to get the answer, but i don't understand the thinking of how to go about the questoin in terms of CREATING the THREE inequalities..

So how exactly do i... evaluate the different possibilites can some one give me something to run with or think about, so i can solve this :(
 
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  • #2
Plutonium88 said:

Homework Statement


Solve
|3x-7|-|x-8|>4



The Attempt at a Solution



so i made columns... and using the columns i made a number line..

7/3 on the left as a point, with a column on its left, and 8 with a column on its right and sharing a coumn in the middle with 7/3

so i have..

|3x-7| => (3x-7), X>OREQUAL 7/3
-(3x-7) x<7/3


|x-8| => (x-8) x>or equal 8
-(x-8) x< 8

* i algebraeicly solved 3 different inequalities after this
1. -(3x-7)-[-(x-8)]>4 (this was not crossed out)-- the answer was crossed x<-2
Unfortunately, you left out the crucial part- HOW you got "-2" as the answer. Distributing the "-"s, -3x+ 7+ x- 8= -2x- 1> 4. Can you solve that?

2. -(3x-7) - (x-8)>4 (this WAS CROSSED OUT)
3. (3x-7) - (x-8) >4 (this was not crossed out) - the answered was crossed x>2/3
Again, you haven't shown how you got that. "x> 2/3" is wrong. Where did that "3" in the denominator come from?

i understand i am supposed to compare the three inequalities after to get the answer, but i don't understand the thinking of how to go about the questoin in terms of CREATING the THREE inequalities..

So how exactly do i... evaluate the different possibilites can some one give me something to run with or think about, so i can solve this :(
 
  • #3
Unfortunately, you left out the crucial part- HOW you got "-2" as the answer. Distributing the "-"s, -3x+ 7+ x- 8= -2x- 1> 4. Can you solve that?

- -2x -1 >4
x < -5/3

lol so basically i rushed and made smoe stupid simple agebraeic errors... Uhh i feel really embarassed i didn't look more carefully at this before i posted... x.x
 
  • #4
HallsofIvy said:
Again, you haven't shown how you got that. "x> 2/3" is wrong. Where did that "3" in the denominator come from?

QUOTE]

(3x-7) - (x-8) > 4

3x-7 -x + 8 > 4

2x 1> 4

x > 3/2

lol even when i look at the stepso n my tests.. my steps are actually correct up until i put

x > 2/3

I CANt BELEIVE this right now... these mistakes are so pathetic...man... :'(

Okay so now that i have 2 separate intervals...

Do i plug in my numbers 3/2 and -5/2 to determine if LS> RS and if it is true? then determinme what ever my interval is using interval notation.?

Also here's a link to the structure of how i did the question originally... Please give me some tips on if you tihnk this is a good way to do the question or if you have any other ideas of how to structure it?

http://postimage.org/image/9q1ec1rhj/

(i didn't even show the calulation where i plugged in my numbers to determine LS>RS Originally) i think i just did it in my head and just tried to figure out whether the number was greater or less than 4... i was lazy..

Ah and last but not least, i am really sorry (if you happen to see the image) for the ugliness of my writing. :(
 
Last edited by a moderator:

FAQ: Soling an inequality using Algebraic method

1. How do I solve an inequality using algebraic method?

To solve an inequality using algebraic method, you need to follow three main steps: 1) Simplify the inequality by isolating the variable on one side of the inequality sign. 2) Use the appropriate properties and rules of algebra to manipulate the inequality and solve for the variable. 3) Check your solution by plugging it back into the original inequality.

2. What are the basic rules of algebra that I need to use?

The basic rules of algebra that you will need to use are: the distributive property, combining like terms, adding or subtracting the same number to both sides of the inequality, multiplying or dividing both sides by the same number, and reversing the inequality sign if multiplying or dividing by a negative number.

3. Can I solve an inequality with variables on both sides?

Yes, you can solve an inequality with variables on both sides by following the same steps as solving an inequality with variables on one side. You will need to combine like terms and use algebraic properties to isolate the variable on one side before solving.

4. How do I know if my solution is correct?

To check if your solution is correct, plug it back into the original inequality and see if it makes the inequality true. If it does, then your solution is correct. If it does not, then you may have made a mistake during the solving process.

5. Can I graph the solution to an inequality using algebraic method?

Yes, you can graph the solution to an inequality using algebraic method. You will need to first solve the inequality for the variable and then graph the solution on a number line. If the inequality is strict (using < or >), you will use an open circle on the number line. If the inequality is inclusive (using ≤ or ≥), you will use a closed circle on the number line. Then, you will shade the appropriate region on the number line based on the inequality sign.

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