Question

Which of the following equations has an infinite number of solutions?

a) 3x−5=3x+7
b) 2x+8=2x+8
c) 4x+3=2x−1
d) 7x+9=5x+11

Answer 1

The equation that has an infinite number of solutions is (b) 2x+8=2x+8, since after simplification, it results in the true statement 8=8. The correct answer is (b) 2x+8=2x+8.

Step-by-step explanation:

The equation with an infinite number of solutions is one where, after simplification, results in a true statement (one that is always true regardless of the value of the variable). When we look at the options provided:

• (a) 3x−5=3x+7: Simplifying would lead to a false statement -5=7, which means there are no solutions.
• (b) 2x+8=2x+8: Simplifying would result in 8=8, which is always true, indicating this is the equation with an infinite number of solutions.
• (c) 4x+3=2x−1: Simplifying would lead to 2x=2, which implies a single solution.
• (d) 7x+9=5x+11: Simplifying would lead to 2x=2, which also implies a single solution.

Therefore, the correct answer is (b) 2x+8=2x+8.