Math help please?

Question

Solve the equation.

| 8 x - 56 | + 40 = 72


Solve the inequality.

l x - 4 l - 5 >= 4
Express your answer in interval notation

Answer 1

first

8x-56<0 then |8x-56|=56-8x

so 56-8x+40=72 implies 96-72=8x, or 24=8x, then x=3.

if 8x-56>0 then |8x-56|=8x-56

so 8x-56+40=72 implies 8x=72+16, or 8x=88, then x=11.

|x-4|-5>= 4 implies |x-4|>= 9

then either x-4>=9, that is x>13 or (13, infty)

or x-4<-9 that is x<-5 or (-infty, -5)

Cheers

Answer 2

Given: (8x - 56) + 40 = 72

8x - 56 + 40 = 72
8x -16 = 72
8x = 72 + 16
8x = 88
x = 11.

Given: (x-4) - 5 ≥ 4

(x-4) - 5 ≥ 4
x - 4 - 5 ≥ 4
x - 9 ≥ 4
x ≥ 4 + 9
x ≥ 13

Answer 3

1. |8x-56| + 40 = 72

=> |8x-56| = 32
=> (8x-56) = 32 or -(8x-56) = 32
=> 8x = 88 or 8x = 24
=> x = 11 or x = 3

Check: |8(11)-56| + 40 or |8(3)-56| + 40
= |32|+40 =|-32|+40
= 72 = 72

2. |x-4| - 5 >= 4

=> |x-4| >= 9

=> (x-4) >= 9 or -(x-4) >= 9
=> x >= 13 or -x+4 >= 9
=> x <= -5

Solution: x is an element of
([13,+infinity),(-infinity,-5])

Check:
Use x=13, x=14 or Use x=-5, x=-6
I leave this as an exercise for you.

Answer 4

| 8x - 56 | + 40 = 72

8x - 56 + 40 = 72

8x - 56 + 40 - 40 = 72 - 40 = 32

8x - 56 = 32

8x = 32 + 56 = 88

8x = 88; x = 11


| x - 4 | - 5 > = 4

(Read: x minus 4 absolute minus 5 is greater than or equal to 4?)

| x - 4 | can only result in a positive value

| x - 4 | > = 9 by adding 5 to both sides

so x > = 13 (x is greater than or equal to 13)

Does that work?

Answer 5

Here are the answers:
1) | 8x -56 | = 32
so: 8x -56 = 32, and 8x -56 = -32
so: 8x = 88, and 8x = 24
so: x = 11, and x= 3
so x = 11 or 3

2) | x-4 | >= 9
so: x-4 >= 9, and x -4 <= -9
so: x >= 13, and x <= -5

so x<= -5, or x>= 13

try any value less than -5 or greater than 13 and it will work.

Answer 6

| 8 x - 56 | + 40 = 72
| 8 x - 56 | = 72 -40 = 32
Either 8 x - 56 = 32
then 8 x = 88
so : x = 11
Or - 8 x + 56 = 32
then - 8 x = - 24
so : x = 3
S.S = { 3 , 11 }
-----------------------------------------
l x - 4 l - 5 >= 4
then l x - 4 l>= 9
Either x - 4 >= 9
then x >= 13
Or - x + 4 >= 9
then -x >= 5
So: x<= 5
S.S : R - ] 5 , 13 [
Where R is the real no. system
] [ is an open interval

Answer 7

(8x-56)+40=72

1. Subtract 40 from both sides of the equal sign.
2. Your new equation is (8x-56)=32
3. Add 56 to both sides of the equation
4. Your new equation is 8x=88
5. Divide both sides by 8.
6. Answer is x=11

Answer 8

I looked at the answers and they are all wrong.

The first one is very obvious :

l x - 4 l - 5 >= 4

Just try to think what this equation is saying

It says :
some number MINUS 5 is bigger than 4

That is impossible dont you think ?
What number can possibly be bigger than FOUR if you subtract FIVE from it

Ok with this information you can probably solve the next equation yourself

| 8 x - 56 | + 40 = 72

Answer 9

1) 8x-56 = 32; 8x = 88; x = 11

2) x - 4 >= 9; x >= 13

Answer 10

8x-56+ 40= 72
8x=88
x=11

x-4-5>=4
x-9>=4
x>=13