7. | 3x - 2 | = 8 and | x + 1 | = 1
What value of x satisfies both equations above?
please show your work. I do notunderstand this.
Thank You
If |x+1| = 1,
x+1 is either 1 or -1, so
x = 0 or -2
Does either of those values satisfy the other equation?
no they don't..I thought these were easy normally - feeling confused
Steve is it no solution?
Did you try the values?
x=0
|3x-2| = |3*0-2| = |-2| = 2
x=-2
|3x-2| = |3(-2)-2| = |-6-2| = |-8| = 8
This is the solution.
To solve this system of equations, you need to find the value of x that satisfies both equations simultaneously.
Let's start with the first equation:
|3x - 2| = 8
To remove the absolute value, we need to consider two cases: when the expression inside the absolute value is positive, and when it is negative.
Case 1: (3x - 2) is positive
If (3x - 2) is positive, then the equation becomes:
3x - 2 = 8
Now, let's solve for x in this case:
3x = 8 + 2
3x = 10
x = 10/3
Case 2: (3x - 2) is negative
If (3x - 2) is negative, then the equation becomes:
-(3x - 2) = 8
Now, let's solve for x in this case:
-3x + 2 = 8
-3x = 8 - 2
-3x = 6
x = 6/(-3)
x = -2
So, in the first equation, we have two potential solutions: x = 10/3 or x = -2.
Now let's move on to the second equation:
|x + 1| = 1
Again, we'll consider two cases: when (x + 1) is positive and when it is negative.
Case 1: (x + 1) is positive
If (x + 1) is positive, then the equation becomes:
x + 1 = 1
Now, let's solve for x in this case:
x = 1 - 1
x = 0
Case 2: (x + 1) is negative
If (x + 1) is negative, then the equation becomes:
-(x + 1) = 1
Now, let's solve for x in this case:
-x - 1 = 1
-x = 1 + 1
-x = 2
x = 2/(-1)
x = -2
So, in the second equation, we have two potential solutions: x = 0 or x = -2.
Now, we need to find the value of x that satisfies both equations simultaneously.
By comparing the solutions we obtained from each individual equation, we can see that x = -2 is a solution that satisfies both equations.
Therefore, the value of x that satisfies both equations is x = -2.