Question

For which value of c will the equation 2x - 5 = 2x - c

have an infinite number of solutions?
A 3
B
4
с 5
D) 6

Answer 1

To have an infinite number of solutions, the equation 2x - 5 = 2x - c must be an identity, meaning that both sides of the equation are always equal, regardless of the value of x. Therefore, the value of c should be any real number since the value of c does not affect the equation.

Step-by-step explanation:

To have an infinite number of solutions, the equation 2x - 5 = 2x - c must be an identity, meaning that both sides of the equation are always equal, regardless of the value of x. This can only happen if the coefficients of x on both sides of the equation are equal. In this case, the coefficient of x is 2. Therefore, for the equation to have an infinite number of solutions, the value of c should be any real number since the value of c does not affect the equation.

For example, if we substitute c = 3 into the equation, we get: 2x - 5 = 2x - 3. Simplifying this, we see that 2x - 5 is equal to 2x - 3 for any value of x, so there are infinitely many solutions.

Learn more about Infinite Solutions in Equations