An Algebra Question...?

1. |x+3| - 4 = -1
The first step is add 4 on both sides
|x+3| - 4 = -1
+4 +4
-----------------------
|x+3| = 4-1
|x+3| = 3
Now, the | | <-- represent absolute value. absolute value is the distance from 0 on a number line. to find it i guess you could just treat it like a normal expression and make your answer positive. for example;
|-4| = 4.
|1293123| = 1293123
so if x+3 = 3
x = 0 right?
well the distance 0 is from 0 is 0. so [x = 0] !

2. -4 |5+2x| = -16
Okay, for this one it would be easier to divide -4 on both sides first. remember it is always easier to isolate the expression that needs to have the absolute value taken.
so
-4 |5+2x| = -16
|5+2x| = 4
5+2x = 4
2x = -1
x = - 1/2
|x| = 1/2 Right!?

Alright, try the 3rd one for yourself, divide first and solve!
Hope that was clear :x!
Goodluck!

sorry dude i can only do the 2nd one for you because today i have no time left.
2) -4 [5+2x] = -16

-20 -8x = -16
-8x = -16 + 20
x= 4/8 => 1/2

1) |x+3|-4=-1
OR x + 3 = 3 or -- 3 giving x = 0 or x = -- 6
2) -4 |5+2x|=-16
OR 5 + 2x = 4 or -- 4 giving x = (4--5)/2 = --1/2 or x = (--4--5)/2 = --9/2
3) -6 |10-2x|=2
OR 10 -- 2x = -- 1/3 or 1/3 giving x = (10+1/3)/2 = 5 1/6 or x = (10--1/3)/2 = 4 5/6

Question 1
| x + 3 | = 3

x + 3 = 3
OR
x + 3 = - 3

x = 0 , x = - 6

Question 2
| 5 + 2x | = 4

5 + 2x = 4
OR
5 + 2x = - 4

x = - 1/2 , x = - 9/2

Question 3
| 10 - 2x | = - 1/3

Has no solution

Could it be - 6 |10 - 2x | = - 2 ?????
| 10 - 2x | = 1/3

10 - 2x = 1/3
OR
10 - 2x = - 1/3

2x = 9⅔ , 2x = 10⅔
x = 29/6 , x = 16/3

1)
|x + 3| - 4 = -1
|x + 3| = -1 + 4
|x + 3| = 3
x + 3 = ±3

x + 3 = 3
x = 3 - 3
x = 0

x + 3 = -3
x = -3 - 3
x = -6

∴ x = -6 , 0

= = = = = = = =

2)
-4|5 + 2x| = -16
|2x + 5| = -16/-4
|2x + 5| = 4
2x + 5 = ±4

2x + 5 = 4
2x = 4 - 5
2x = -1
x = -1/2 (-0.5)

2x + 5 = -4
2x = -4 - 5
x = -9/2 (-4.5)

x = -9/2 (-4.5) , -1/2 (-0.5)

= = = = = = = =

3)
-6|10 - 2x| = 2
|10 - 2x| = 2/-6
|10 - 2x| = -1/3 (|x| must be equal to positive number)
(no solutions)

1) |x+3|-4=-1
OR x + 3 = 3 or -- 3 giving x = 0 or x = -- 6
2) -4 |5+2x|=-16
OR 5 + 2x = 4 or -- 4 giving x = (4--5)/2 = --1/2 or x = (--4--5)/2 = --9/2
3) -6 |10-2x|=2
OR 10 -- 2x = -- 1/3 or 1/3 giving x = (10+1/3)/2 = 5 1/6 or x = (10--1/3)/2 = 4 5/6

|x+3| = -1 + 4 = 3
x+3 = 3 or x+3 = -3
x=0 x= -6
put these values in the equation to verify..
similarly all other equations can be solved easily!

1.) |x+3|-4=-1
-4x-12=-1
-4x=-1+12
-4x=11
-4x/-4=11/-4
x=-2 3/4

2.)-4|5+2x|=-16
-20-8x=-16
-8x= 20-16
-8x= 4
-8x/-8= 4/-8
x= - 1/2

3.) -6 |10-2x|=2
-60+12x=2
12x=2+60
12x/12=62/12
x= 5 2/12 or 5 1/6