Question

Determine the value of x in the equation. Five-sixths times the quantity x plus 2 minus three-sixths times x equals two-sixths times the quantity x plus 5.

a. Infinite solutions
b. No solution
c. x = 1
d. x = 3

Answer 1

To determine the value of x in the equation, we simplify the equation step by step and find that there is no solution.

Step-by-step explanation:

To determine the value of x in the equation, we need to simplify the equation step by step.

1. Start by distributing the coefficients: 5/6 * (x + 2) - 3/6 * x = 2/6 * (x + 5)
2. Simplify each side of the equation: (5/6)x + 5/6 - (3/6)x = (2/6)x + 10/6
3. Combine like terms: (5/6 - 3/6)x + 5/6 = (2/6)x + 10/6
4. Further simplify: (2/6)x + 5/6 = (2/6)x + 10/6
5. Subtract (2/6)x from both sides: (2/6)x - (2/6)x + 5/6 = (2/6)x - (2/6)x + 10/6
6. Simplify: 5/6 = 10/6

The equation is not valid and both sides are not equivalent.

Therefore, the answer is b. No solution.