Question

Solve for x: 3/4 + x = 2x - x + ? (add a number so that the equation has infinite solutions).

a) 3/4
b) 0
c) 1/2
d) 2

Answer 1

To make the equation 3/4 + x = 2x - x + ? have infinite solutions, we add the number that makes both sides identical. Simplifying both sides, we find that adding 3/4 will achieve this, making (a) 3/4 the correct answer.

Step-by-step explanation:

The equation given is 3/4 + x = 2x - x + ? and we need to find the number that can be added to make this equation have infinite solutions. To have infinite solutions, the equation must become an identity, meaning both sides are exactly the same. For this to happen, the term we add must result in the x terms and constant terms being same on both sides of the equation. Let's simplify the equation first:

• Combine like terms on the right side: 2x - x becomes just x.
• Now the equation is: 3/4 + x = x + ?
• To make this an identity (the same on both sides), we need the constant terms to be equal, so ? must be 3/4.

Therefore, the correct answer is (a) 3/4.