I already asked this question once about the absolute value of 3x-2=8 and absolute vale x+1=1....value of x?...and the answer I received was does 0 or -2 satisfy both ....they dont...so is it no solution?
Please help - I do not understand this problem....Thanks
If I recall the question that Steve already answered for you , it was
|3x-2| = 8 and | x+1| = 0
What he did was to solve the easier of the two, and then asked you to check if these answers satisfied the first.
Why did you not do that?
if |x+1| = 1
then x+1 = 1 or x+1 = -1
x = 0 and x = -2
now test those in the first
if x = 0
LS = | 3(0) - 2|
= |-2| = 2
but RS = 8 , so x = 0 does NOT work in both
if x = -2
LS = |(3(-2) - 2|
= |-8|
= 8 = RS ,
so our solution is x = -2 , since it works in both equations.
Now I understand - I only asked for an explanation...I would have put those into place if I wasn't confused...thanks for the help..didn't mean to bother anyone!
To determine the value of x, we need to solve the equations involving absolute values separately. Let's start by considering the equation |3x - 2| = 8.
To solve this equation, we need to equate the expression inside the absolute value (3x - 2) to both the positive and negative value of 8:
1) 3x - 2 = 8
2) -(3x - 2) = 8
Solving equation 1:
Adding 2 to both sides, we get:
3x - 2 + 2 = 8 + 2
3x = 10
Dividing both sides by 3, we get:
x = 10/3
Solving equation 2:
Distributing the negative sign:
-(3x) + 2 = 8
Subtracting 2 from both sides:
-(3x) + 2 - 2 = 8 - 2
-(3x) = 6
Dividing both sides by -3 (remember to change the sign of the inequality when dividing by a negative), we get:
x = -2
Now let's consider the equation |x + 1| = 1.
To solve this equation, we need to equate the expression inside the absolute value (x + 1) to both the positive and negative value of 1:
1) x + 1 = 1
2) -(x + 1) = 1
Solving equation 1:
Subtracting 1 from both sides:
x + 1 - 1 = 1 - 1
x = 0
Solving equation 2:
Distributing the negative sign:
-(x) - 1 = 1
Adding 1 to both sides:
-(x) - 1 + 1 = 1 + 1
-(x) = 2
Dividing both sides by -1 (remember to change the sign of the inequality when dividing by a negative), we get:
x = -2
Now, let's check which values of x satisfy both equations:
For |3x - 2| = 8:
- When x = 10/3, |3(10/3) - 2| = |10 - 2| = |8| = 8, which satisfies the equation.
- When x = -2, |3(-2) - 2| = |-6 - 2| = |-8| = 8, which also satisfies the equation.
For |x + 1| = 1:
- When x = 0, |0 + 1| = |1| = 1, which satisfies the equation.
- When x = -2, |-2 + 1| = |-1| = 1, which also satisfies the equation.
Therefore, both x = 10/3 and x = -2 satisfy both equations.