Question

Solve for the unknown variable. 9x-75-3x=6x+60 Stuck?

a. No solution
b. All real numbers
c. Cannot be determined

Answer 1

To solve the equation, we simplify and combine like terms to find that it leads to a contradiction (-75 = 60), which means there is no solution to the equation. The correct answer is option (a) No solution.

Step-by-step explanation:

To solve for the unknown variable in the equation 9x - 75 - 3x = 6x + 60, we first combine like terms. The equation simplifies as follows:

1. Combine the x-terms on the left-hand side: 9x - 3x = 6x, which simplifies to 6x.
2. The equation now looks like: 6x - 75 = 6x + 60.
3. Now, subtract 6x from both sides to move all the x-terms to one side: 6x - 6x - 75 = 6x - 6x + 60, which simplifies to -75 = 60.
4. Since -75 does not equal 60, this is a contradiction, indicating there is no solution to this equation. The correct answer is (a) No solution.

It's important to look out for such contradictions as they mean that the equation has no solution, and no value of x would satisfy the given equation.