What is the solution for absolute value of -1 + x = 5
I think the two solutions are x = 6 and x = (-4)
Correct. You could actually check these problems yourself by plugging in your answers.
Thank you- I just wanted to double check
To find the solutions for the absolute value equation | -1 + x | = 5, we need to remember the definition of absolute value. The absolute value of a number x is the distance between x and zero on the number line. Therefore, | x | = x if x is greater than or equal to zero, and | x | = -x if x is less than zero.
In our equation, |-1 + x | = 5, we have the expression -1 + x inside the absolute value brackets. We need to consider two cases, one where -1 + x is greater than or equal to zero, and the other where -1 + x is less than zero.
Case 1: -1 + x ≥ 0
Solving this inequality, we have x ≥ 1. Therefore, in this case, | x | = x.
Substituting x = 1 into the equation |-1 + x | = 5, we get |1 - 1| = 5, which simplifies to |0| = 5.
As |0| equals zero, this equation has no solutions in this case.
Case 2: -1 + x < 0
Solving this inequality, we have x < 1. Therefore, in this case, | x | = -x.
Substituting x = -4 into the equation |-1 + x | = 5, we get |-1 + (-4)| = 5, which simplifies to |-5| = 5.
As |-5| equals five, this equation has one solution in this case.
Therefore, the solution to the equation | -1 + x | = 5 is x = -4.