What am i doing wrong with my math problem? (algebra)?

Question

This is the problem and my wor (<_ is smaller than or equel to; * is multiply)

-7<_ 3-x <5
-3 -3 -3
-11<_ -x <2
*-1 *-1 *-1
11>_ x > -2 <----final answer

our teacher asks us to check the odd numbers of our homework in the back of the book were it lists the odd numbers. the answer in the book gives me

-2 < x <_ 10

what did i do wrong?

please explan it the way i did

thanks!

thanks! i cannot believe i got that wrong. I was thinking 3 was a 4!

Answer 1

in your second line, when you subtract 3 from all terms
-7 -3 should be -10 and not -11.
so that line should be
-10 <_ -x < 2
and after that you are doing fine.
your answer is the same as in the book except it is written the other way around,
i.e. you are getting the answer as x is less than or equal to 10 but greater than -2
and your book is also saying the same thing that x is greater than -2 but less than or equal to 10.

Answer 2

To simply it more you could have seprated it.


-7<= 3-x and 3-x< 5
(subtract 3 from each side)

-10<=-x -x< 2 (Multiply each of these by negative 1 to get rid of the negative x, you flip the signs do to the fact you multiplying by a negative)


thus becoming...


-2 < x <= 10


This is really as simple as you can get, how can you have problems with this basic algebra.

Answer 3

-7 - 3 = -10, so the number on the left of your answer is wrong.

You are correct to multiply (or divide) by -1, and you correctly switched the direction of the inequality.

That would give you -10 is greater than or equal to x, which is greater than or equal to -2. This is absolutely equivalent to your book's answer, which is just written in less than form.

Answer 4

When you take the 3 from all sections you should have ended up with -10 on the first one.
Secondly, two divided by -1 is -2. hope this helps.

Answer 5

-7 <_ 3-x <5
-3 -3 -3
-10 <_ -x < 2
*-1 *-1 *-1
10 >_ x > -2

all you did wrong is -7 -3 is -10