ok help me math?!?!?!?

Question

Ok so i did like all these problems but i got ALL of them wrong. and my wrong answers make so much sence to me so i have no idea how there wrong. Could you please show the steps for these problms/exmplain. I have a terrible math teacher who doesnt teach anything. really frustrating

1. |4-x| - 10 = 1

2. |2x-5| = 3x + 4

3. |3x| -4 >8

4. |3x-6|+3<15

5. 7|8-3x| = 21x-49

6. 1/4|4x+7|= 8x+16

7. 1/11|2x-4| + 10<(greater then or equal too)11

Answer 1

|absolute value| is the distance from zero without taking direction into account. Except for 0, there are always two numbers that have the same absolute value +something and -something. Work the | | once as it is and once as a negative.
Here are the first three

1. |4-x| - 10 = 1
|4-x| = 11
4-x = 11
-7 = x (first answer)
-(4-x) = 11
14+x = 11
x = 15 (second answer)

2. |2x-5| = 3x + 4
2x - 5 = 3x + 4
-9 = x (first answer)
-(2x-5) = 3x + 4
-2x + 5 = 3x +4
1 = 5x
.2 = x (second answer)

3. |3x| -4 >8
3x - 4 > 8
3x > 12
x > 4 (first answer)
-3x -4 > 8
-3x > 12
-x > 4
x < -4 (second answer)

Now you try.

Answer 2

For absolute values, the best thing to do is get the absolute value part on one side of the equation on its own. You then have to consider the two possible values - when it is positive and when it is negative.

For the first one:

|4-x| - 10 = 1
|4-x| = 11

So, 4-x = 11 or 4-x = -11
Therefore, x = -7 or x = 15

With an inequality it is more complicated.

For your third question:

|3x| - 4 > 8
|3x| > 12

So, 3x > 12 or 3x < -12.
Therefore, x > 4 or x < -4

Note how we have to change the sign around for the negative answer. If we said 3x > -12 then 3x may equal (say) 3 which is greater than -12 but does not satifsy our original equation.

For something like your fifth question, it works the same as the first one:

7|8-3x| = 21x - 49
|8-3x| = 3x - 7

So, 8-3x = 3x-7 or 8-3x = -(3x-7)

For the first one:
8-3x = 3x-7
8 +7 = 3x + 3x
15 = 6x
x = 15/6

For the second one we have problems:
8-3x = -(3x-7)
8-3x = -3x + 7
8 - 7 = -3x + 3x
1 = 0 D'oh!

So there is only one answer for this problem - x=15/6.

Answer 3

1.(4-x)-10=1
(4-x)=1+10
4-x=11
-x=11-4
-x=7
x=-7
2.(2x-5)=3x+4
2x-3x=4+5
-x=9
x=-9
3.(3x)-4>8
3x>8+4
3x>12
x>12/3
x>4
4.(3x-6)+3<15
3x-6<15-3
3x-6<12
3x<12+6
3x<18
x<18/3
x<6
5.7(8-3x)=21x-49
8-3x=(21x-49)/7
8-3x=3x-7
-3x-3x=-7-8
-6x=-15
6x=15
x=15/6
x=5/2
6.1/4(4x+7)=8x+16
(4x+7)=(8x+16)4/1
4x+7=32x+64
4x-32x=64-7
-28x=57
-x=57/28
x=-57/28
7.1/11(2x-4)+10<11
1/11(2x-4)<11-10
1/11(2x-4)<1
(2x-4)<(1)11/1
2x-4<11
2x<11+4
2x<15
x<15/2