|10x - 1| = x - 10
A. -1, 1
B. 1
C. -1
D. No solution
D. No solution
then either
10x-1=x-10 OR -10x +1 = x-10
9x = -9 or -11x = -11
x = -1 or x = +1
BUT, by definition |of anything| ≥0
so x-10≥0
x ≥ 10
So there is no solution
thank you
To solve the equation |10x - 1| = x - 10, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: Assume that 10x - 1 ≥ 0, meaning 10x - 1 is positive. In this case, the absolute value is unnecessary, so we can write the equation as 10x - 1 = x - 10.
10x - 1 = x - 10
9x = -9
x = -1.
Therefore, if 10x - 1 is positive, the solution is x = -1.
Case 2: Assume that 10x - 1 < 0, meaning 10x - 1 is negative. In this case, we need to remove the negative sign from the equation, so we can write the equation as -(10x - 1) = x - 10.
-(10x - 1) = x - 10
-10x + 1 = x - 10
-11x = -11
x = 1.
Therefore, if 10x - 1 is negative, the solution is x = 1.
Since we found two distinct solutions for different conditions, the correct answer to the equation |10x - 1| = x - 10 is x = -1, 1. Therefore, the correct option is A. -1, 1.