Steve I already asked you the question about the absolute value of 3x-2=8 and absolute vale x+1=1....value of x...and your answer was does 0 or -2 satisfy both ....they dont...so is it no solution?
Yes, based on the equations, there is no solution. Let me explain how we can determine this.
To solve the equation |3x - 2| = 8, we need to consider the two cases: (1) when 3x - 2 is positive, and (2) when 3x - 2 is negative.
Case 1:
When 3x - 2 is positive, we can simply remove the absolute value symbols. So we have 3x - 2 = 8. Solving this equation gives us 3x = 10, and dividing both sides by 3, we get x = 10/3, which is approximately 3.33.
Case 2:
When 3x - 2 is negative, the absolute value |3x - 2| will become -(3x - 2). So we have -(3x - 2) = 8. We can multiply -1 to both sides of the equation to remove the negative sign, resulting in 3x - 2 = -8. Solving this equation gives us 3x = -6, and dividing both sides by 3 gives x = -2.
Now, let's consider the equation |x + 1| = 1. Similarly, we have two cases:
Case 1:
When x + 1 is positive, we can remove the absolute value symbols, giving us x + 1 = 1. Solving for x, we find x = 0.
Case 2:
When x + 1 is negative, the absolute value |x + 1| will become -(x + 1). We have -(x + 1) = 1. Multiplying -1 to both sides, we get x + 1 = -1. By subtracting 1 from both sides, we find x = -2.
Now, we compare the solutions from both equations. We have x = 10/3 (approximately 3.33), -2, 0 as potential solutions. However, the value of x = 10/3 satisfies the first equation but not the second equation. Similarly, the value of x = 0 satisfies the second equation but not the first equation. The only value that satisfies both equations is x = -2.
Therefore, the only solution to the system of equations is x = -2, and there is no other value of x that satisfies both equations.