algebra 1 help...?

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1)x=+-6
2)x=4,-14/3

You are dealing with absolute value. The absolute value of 1 is 1 and the absolute value of -1 is 1.


1. |x| =6 means x is either 6 or -6 since the absolute value of both number is 6.

2. Set it up by saying 3x + 2 = 14 or 3x + 2 = -14 since the value inside the absolute value can either be 14 or -14.
Solving the first gives you x=4 the second is x= -16/3.

3. First, divide both sides by 5. Now you have |x + 1| = 2
So x + 1 = 2 or x + 1 = -2. Solving both gives you x is 1 or x = -3.

4. First, subtract 10 from both sides. Now you have |x - 2| = 2. So x -2 = 2 or x - 2 = -2. Solving both for x means x is 4 or x = 0.

5. This has no solution because the absolute value of a number cannot be negative.

6. Add 4 to both sides of the equation. Now you have |2x + 6| = 24. So 2x + 6 = 24 or 2x + 6 = -24. Solving for x for both equations, gives you x = 9 or x= -15.

7. Subtract 6 from both sides of the equation, gives you -3|2x +6| = -6. Now divide both sides by -3, you get |2x + 6| = 2, so 2x + 6 = 2 or 2x + 6 = -2, solving both for x gives you x = -2 or x =-4.

8. There is no answer for this because whatever you put in for x, |x + 2| will be a positive number, so 10 minus a positive number will never give you 12.

if there is mod there u should keep mod on LHS and other on RHS. when u r removing mod on LHS, u should remove the signs on the mod if they are negetive . for eg i will show u your prolems done.

1.|x|=6
x=6

2.|3x+2|=14
3x+2=14
3x=14-2 => 3x=12 => x=12/3 => x=4


3. - 5| x + 1| = -10
|x+1|= -10 / -5
|x+1|= 2
x+1=2
x=2-1
x=1

4. |x - 2| + 10 = 12
|x-2|=12-10
|x-2|=2
x-2=2
x=2+2
x=4

5. |x| = - 5
x=-5


6. |2x + 6| - 4 = 20
|2x + 6|=20-4
|2x + 6| = 20 +4
|2x + 6| = 24
2x+6 = 24
2x = 24 - 6
2x = 18
x = 18 / 2
x = 9

7. 6 - 3|2x + 6| = 0
-3|2x + 6| = -6
|2x + 6| = -6 / -3
|2x + 6| = 2
2x + 6 = 2
2x = 2 - 6
2x = -4
x= -4 / 2
x= -2

8. 10 - |x + 2| = 12
-|x + 2| = 12 - 10
-|x + 2| = 2
|x + 2| = -2
x + 2 = -2
x = -2 - 2
x= -4

The lxl is absolute value, or distance from zero. Basically it's the same as having that number in parenthesis where you solve that part first, except when you solve it you make it positive.

EX. #3. Distribute -5 into the "| |" making it |-5x+1|=-10.
Then make it positive and take the "| |" away and you get 5x+1=-10 Then solve like a normal problem, and you're on your own there.

Hope it helps!

1)
|x| = 6
x = ±6

= = = = = = = =

2)
|3x + 2| = 14
3x + 2 = ±14

3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4

3x + 2 = -14
3x = -14 - 2
3x = -16
x = -16/3

∴ x = -16/3 , 4

= = = = = = = =

3)
-5|x + 1| = -10
|x + 1| = -10/-5
|x + 1| = 2
x + 1 = ±2

x + 1 = 2
x = 2 - 1
x = 2

x + 1 = -2
x = -2 - 1
x = -3

∴ x = -3 , 2

= = = = = = = =

4)
|x - 2| + 10 = 12
|x - 2| = 12 - 10
|x - 2| = 2
x - 2 = ±2

x - 2 = 2
x = 2 + 2
x = 4

x - 2 = -2
x = -2 + 2
x = 0

∴ x = 0 , 4

= = = = = = = =

5)
|x| = -5 (impossible)

= = = = = = = =

6)
|2x + 6| - 4 = 20
|2x + 6| = 20 + 4
|2x + 6| = 24
2x + 6 = ±24

2x + 6 = 24
2x = 24 - 6
2x = 18
x = 18/2
x = 9

2x + 6 = -24
2x = -24 - 6
2x = -30
x = -30/2
x = -15

∴ x = -15 , 9

= = = = = = = =

7)
6 - 3|2x + 6| = 0
-3|2x + 6| = -6
|2x + 6| = -6/-3
|2x + 6| = 2
2x + 6 = ±2

2x + 6 = 2
2x = 2 - 6
2x = -4
x = -4/2
x = -2

2x + 6 = -2
2x = -2 - 6
2x = -8
x = -8/2
x = -4

∴ x = -4 , -2

= = = = = = = =

8)
10 - |x + 2| = 12
-|x + 2| = 12 - 10
-|x + 2| = 2
|x + 2| = -2 (impossible)

|x| represents the absolute value of x. absolute value is nothin but the "positive" value. i.e if x = -5, then the absolute value of x is 5. Note that the absolute value of 5 is also 5.
Now, in ur problems, we have work the solutions backwards.
it is given that |x|=6 in the first problem.
that means x could have been -6 or 6 because the |x| of both -6 and 6 is equal to 6.
similarly, there will be 2 solutions for every question.

question 1)
|x| = 6
solution 1: x = -6
solution 2: x = +6

question 2)
|3x+2| = 14
or 3x+2 = +/- 14
solution1: 3x+2 = -14
x = -16/3
solution2: 3x+2 = 14
x = 4

question3)
-5|x+1| = -10
or |x+1| = 2 ( before applying the 2 cases, you have to make sure that everything is in the form |x| = something

solution 1: x+1 = -2
x = -3
solution 2: x+1 = 2
x = 1

question 4)
|x-2| + 10 = 12
|x-2| = 2
solution 1: x = 0
solution 2: x = 4

question 5)
no solution exists because |x| can never be equal to -5.
x can be equal to -5 but |x| is always a positive value.

question 6)
|2x+6| - 4 = 20
or |2x+6| = 24
solution 1: x = 9
solution 2: x =15

question 7)
6 - 3|2x+6| = 0
or 3|2x+6| = 6
or |2x+6| = 2
solution 1: x = -2
solution 2: x = -4

question 8)
10 - |x+2| = 12
|x+2| = -2
No solution exists because absolute value cannot be negative.

1.|x| = 6,
x=+/- 6

Similarly i will use the same method.
2.3x+2 = +14 or 3x+2 = -14
3x=12 or 3x = -16
x=4 or x=-16/3

3.-5|x+1| = 14
|x+1| = -14/5
x+1= -14/5 or x+1 = 14/5
x=-19/5 or x=9/5

4.|x-2| + 10 = 12
|x-2| = 2
x-2 = 2 or x-2 = -2
x=4 or x=0

5.|x| = -5,
x=5 or -5

6.|2x+6| = 24
2x+6 = 24 or 2x+6 = -24
2x=18 or 2x= -30
x=9 or x=-15

7.6-3|2x+6|=0
-3|2x+6| = -6
|2x+6| = 2
2x+6 = 2 or 2x+6=-2
2x=-4 or 2x=-8
x=-2 or x=-4

8.10-|x+2| = 12
|x+2| = -2
x+2 = -2 or x+2= 2
x=-4 or x=0

These are answers for your questions.
I hope they will be useful to you.

The lines around the numbers and variables means absolute value which is the distance a number is from zero on a number line. Absolute value is always positive unless the negative sign is outside the lines.
1. either positive or negative six works because both are six away from zero.
2. only four works because negative four would give you an answer of 10.
3.1 or -3 works. First divide both sides by negative five and the solve the equation. Check to find answers that dont fit the equation.

I'm pretty sure that I know how to do it!:] I just finished this class.
If x is inside the two lines, then there are two answers,
The two lines means that it's the distance that it is from zero.
which means that
|-6|=6
and
|6|=6
and so that is your answer to number one.
x= -6 & 6

for two, it's a bit more complicated, you have to solve it once as if 14 is positive and once as if 14 is negative.
(When you deal with the seperate equations, you take away the ||)
and so, if we were dealing with the positive one, you would minus the two from both sides, giving you 3x=12, then you divide by 3, giving you x=4.
Then you solve it with the 14 as a negative, and then the two answers are your answer to the problem.


sorry if that was long and confusing! xDD

1. x = + or - 6
2. 3x + 2 = 14 3x = 12 x= 4
or 3x + 2 = -14 3x = - 16 x=-16/3
3. x+1 = 2 x=1
or x + 1 = -2 x = -3

1) X=6

2)subtract 2 from each side 3x=12 divide 3 and x=4

3)add 5 to both sides x+1= -5 x= -6

you can do the same for the rest