three fourths times the quantity x plus 6 end quantity minus one fourth times x equals two fourths times the quantity x plus 9 end quantity
a x = 1
b x = 2
c No solution
d Infinite solutions
Let's solve the equation step by step:
First, we simplify the equation:
(3/4)(x + 6) - (1/4)x = (2/4)(x + 9)
Next, we clear the fractions by multiplying all terms by 4:
4(3/4)(x + 6) - 4(1/4)x = 4(2/4)(x + 9)
3(x + 6) - x = 2(x + 9)
Expanding and simplifying, we get:
3x + 18 - x = 2x + 18
Combine like terms:
2x + 18 = 2x + 18
As we can see, both sides of the equation are equal. This means that the equation is true for any value of x. Therefore, the equation has infinite solutions.
Therefore, the answer is d) Infinite solutions.