Question

20. Which equation has no solution?

[A] 9y+9 = 11y-2y+9
[B] 7x+30 = x+6(5+x)
[C] -5x+9 = 2x+9-7x
[D] 7x-6 = x+6(5+x)

Answer 1

To determine which equation has no solution, we need to analyze each equation and look for contradictory statements. The equation that has no solution is 7x-6 = x+6(5+x).

Step-by-step explanation:

To determine which equation has no solution, we need to simplify each equation and see if we can get a contradictory statement. Let's analyze each equation:

1. 9y+9 = 11y-2y+9: Combining like terms, we get 9 = 9y. However, there is no value of y that satisfies this equation, so there is no solution.
2. 7x+30 = x+6(5+x): Expanding the expression on the right side, we get 7x+30 = x+30+6x. Simplifying further, we have 7x+30 = 7x+30. This equation is true for all values of x, so it has infinite solutions.
3. -5x+9 = 2x+9-7x: Combining like terms, we have -5x+9 = -5x+9. This equation is true for all values of x, so it also has infinite solutions.
4. 7x-6 = x+6(5+x): Expanding the expression on the right side, we get 7x-6 = x+30+6x. Simplifying further, we have 7x-6 = 7x+30. Subtracting 7x from both sides, we get -6 = 30. This is a contradictory statement, so there is no solution.

Thus, the equation that has no solution is 7x-6 = x+6(5+x).

Learn more about Equations with no solution