Question

Which equation has no solution?

1) |2x – 1| = 9
2) |5 – 3x| = 7
3) |–x – 3| = -4
4) |–x + 9| = -6

Answer 1

The equation |–x – 3| = -4 has no solution.

Step-by-step explanation:

To determine which equation has no solution, we need to check if the absolute value expressions on both sides of the equation can equal each other. If the absolute values can never be equal, then the equation has no solution.

Let's analyze each equation:

1. |2x – 1| = 9: This equation can be solved by isolating the absolute value expression and solving for x. The solution is x = 5 or x = -4, so this equation has solutions.
2. |5 – 3x| = 7: This equation can be solved by isolating the absolute value expression and solving for x. The solution is x = -2/3, so this equation has a solution.
3. |–x – 3| = -4: This equation can be rewritten as |-x - 3| = 4, since the absolute value of a negative number is positive. The absolute value expression can never equal 4, so this equation has no solution.
4. |–x + 9| = -6: This equation can be rewritten as |-x + 9| = 6, since the absolute value of a negative number is positive. The absolute value expression can never equal 6, so this equation has no solution.

Therefore, the equation |–x – 3| = -4 has no solution.