Final answer:
To determine which equation has no solution, we need to solve each equation and see if there is a value of x that satisfies the equation. None of the given equations have no solution, as they all have values of x that satisfy the equations.
Step-by-step explanation:
To determine which equation has no solution, we need to solve each equation and see if there is a value of x that satisfies the equation. Let's go through each option:
1) |–x – 3| - 4 = 1:
Remove the absolute value: -x - 3 - 4 = 1
-x - 7 = 1
-x = 8
x = -8
Therefore, this equation has a solution, x = -8.
2) |2x – 1| + 9 = 9:
Remove the absolute value: 2x - 1 + 9 = 9
2x + 8 = 9
2x = 1
x = 1/2
Therefore, this equation has a solution, x = 1/2.
3) |-x + 9| - 6 = -6:
Remove the absolute value: -x + 9 - 6 = -6
-x + 3 = -6
-x = -9
x = 9
Therefore, this equation has a solution, x = 9.
4) |5 – 3x| + 7 = -1:
Remove the absolute value: 5 - 3x + 7 = -1
-3x + 12 = -1
-3x = -13
x = 13/3
Therefore, this equation has a solution, x = 13/3.
None of the given equations have no solution, as they all have values of x that satisfy the equations.