Question

Identify whether each equation has one solution, infinitely many solutions, or no solution.

2(x−5)=2(x−5)
a. No solution
b. One solution
c. Infinitely many solutions
d. Cannot be determined from the information given

Answer 1

The equation 2(x-5)=2(x-5) has infinitely many solutions because it is the same expression on both sides of the equal sign, indicating that they are identical for any value of x.

Step-by-step explanation:

The equation in question, 2(x−5)=2(x−5), is essentially the same expression on both sides of the equal sign, indicating that the two sides are identical no matter what value of x is chosen. To solve this, we simplify the equation:

• Distribute the 2 into the parentheses on both sides: 2*x - 2*5 = 2*x - 2*5
• This simplifies to 2x - 10 = 2x - 10, which is indeed the same expression on both sides.

Since the expressions are identical, any value for x will satisfy the equation, which means that the equation has infinitely many solutions.