Question

9 + 1/2x = 5x - 1. How many solutions does this equation have?

a) One Solution
b) Infinite (many) solutions
c) No solution

Answer 1

The equation has one solution: x = 20/9. Correct option is a.

Step-by-step explanation:

This equation is a linear equation in one variable, x. To determine the number of solutions, we need to solve the equation and see if it has any solutions. Here are the steps:

1. Combine like terms on both sides of the equation: 9 + 1/2x = 5x - 1
2. Subtract 1/2x from both sides: 9 = 5x - 1 - 1/2x
3. Simplify the equation: 9 = 9/2x - 1
4. Add 1 to both sides: 10 = 9/2x
5. Multiply both sides by 2/9 to isolate x: x = 10 * (2/9) = 20/9

Therefore, the equation has one solution: x = 20/9.