What the heck am I doing wrong?

Question

Ok this is a simple algebra problem, but for some reason I can't figure out what I am doing wrong. The problem is:
SOLVE (written in interval notation):

-5x+11/2 is less than or = 7.

The first step is to multiply each variable/number by 2; the common denominator of the two fractions (-5x+11/2 & 7/1). Hence, you would get -10x + 22 is less that or = 14. Then, you would subtract 22 from both sides therefore making -10x less than or = -8. Divide -8 by -10 and the solution therefore is [8/10 to infinity), or 4/5 to infinity if simplified. However, my stinking College Algebra book says the answer is [3/5 to infinity).


Step 1: -5x + 11/2 < or = 7

Step 2: (2)-5x + 2(11) < or = (2)7

Step 3: -10x + 22 < or = 14
- 22 -22

Step 4: -10x < or = -8
/-10 /-10 = 8/10 = 4/5!


HOW COULD IT BE 3/5?!? Any thoughts or advice? Thanks!

Answer 1

11/2 * 2 = 11

You wrote 22.

To get the answer that the textbook had, I wonder if your problem was set up as (-5x + 11) / 2

Was the two the denominator for both -5x and 11? If so, when you multiply by 2, the divide by 2 goes out the window, but the -5x + 11 stays in tact.

-5x + 11 <= 14
-5x <= 3

x >= -3/5

The sign switched since we multiply/divide by a negative number! Good luck! I hope this helped.

Answer 2

II like to work with whole # as much as possible so I would change -5x+11/2 less or =7 to read -5x+5 1/2 less than or =7 then I would substract 5 1/2 from each side would would make the equation -5x less or =7-5 1/2 which will then become -5x less or =1 1/2 then change 1 1/2 back to a fraction which will be 3/2 then divide both sides by 1/5. 1/5 divided in 5/1x equals x less or = 3/2 divided by 1/5 which equals 3/10 therefore, x less or=3/10 answer is 3/10 not 3/5. YOUR MISTAKE WAS THAT YOU TRIED TO MULTIPLY BY THE DEMONATOR 2. does not work.

Answer 3

-5x+11/2 <= 7
-5x <= 7 - 11/2 = (14 - 11)/2 = 3/2
5x >= -3/2
x >= -3/10

Thus the equation is satisfied by any x value from -3/10 up through an indeterminate value often called infinity. It could not be >= 3/5 unless the second term (11/2) were actually (11) and the (7) were actually (14).

Answer 4

every time i tried it i got 3/10

however i see where you made a mistake in your calculation:
Step 1: -5x + 11/2 < or = 7
Step 2: (2)-5x + 2(11) < or = (2)7

In the second step you chose to multiply every value by 2. However instead of 2(11/2), you did 2(11).

Answer 5

Step 2 is where you went wrong.
Here's your calculation: (2)-5x + 2(11) < or = (2)7
Correct method = (2)-5x + 2(11/2) < or = (2)7
You forgot 11/2 and just took it as 11
2(11/2) = 11
Step 3 should be: - 10x + 11 < or = 14
I think you can manage the rest. Best of luck!

Answer 6

-5x+(5.5) (I'll use "<=" for "less than or equal to") 7
- 5.5 -5.5

-5x <= 1.5
/5 /5

-x<=.3
/-1 /-1 (here the sign switches due to dividing by a negative)

x=>-.3 so your answer is x greater than or equal to -.3 I don't see how you get 3/5. I'll try it your way though

when you multiply the entire thing by 2, you get -10x+11 (not 22) <=14

subtract 11 from both sides. -10x<=3

divide by -10 and you get x greater than or equal to -.3 your book is wrong, or you misread the fraction.

Answer 7

your mistake is at step 2. 2*(11/2)=11 not 22.and are you sure that the answer is 3/5? cause i get x>=-3/10

Answer 8

-5x + 11/2 < or = 7

- 11/2 < or = 7

-5x < or = 3/2

-5x/ -5 < or = 1.5 / -5

x < or = -.3


BTW you have to subtract the 11/2, not flip it over.

Answer 9

first step:

-5x +11/2 < or = 7

2nd step:

-5x < or = 7 - 11/2

3rd step:

-5x < or = 7(2) -11/2(2)
-5x < or =14-11
-5x < or =3

4th step

-5x < or =3
x= -3/5

Answer 10

Step two is wrong u r wrong at the LCM part its
2*-5x+11<=2*7
The sum is wierd anyway cauze u still wont get the answer