## Anna is given the equation 3 + 2x = 2x + 3 The replacement set is {2, 3, 4, 5} Anna says the solution is {3}, but the teacher marked her

Question

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.Morbi adipiscing gravdio, sit amet suscipit risus ultrices eu.Fusce viverra neque at purus laoreet consequa.Vivamus vulputate posuere nisl quis consequat.

## Answers ( No )

Answer:The given equation has

infinite number of solutions. This means thatany real numbercan be considered a solution to the given equation.Since the given replacement set {2,3,4,5} consists of real numbers, therefore, the whole set is considered as a solution to the given equation.

This is because, when solving the given equation for x, we will end up with 0 = 0, this means that whatever the value of x is, both sides of the equation will always be equal.

Explanation:To solve for x, we need to isolate the x on one side of the equation.

This can be done as follows:3 + 2x = 2x + 3 (subtract 3 from both sides)

2x = 2x (subtract 2x from both sides)

0 = 0This means that whatever, the value of x is, both sides of the equation will be equal. This means that all real numbers are considered a solution for this equation.

Let’s verify this using the given replacement set {2,3,4,5}:For x = 2:Left hand side: 3 + 2(2) = 3 + 4 = 7

Right hand side: 2(2) + 3 = 4 + 3 = 7

Both sides are equal.For x = 3:Left hand side: 3 + 2(3) = 3 + 6 = 9

Right hand side: 2(3) + 3 = 6 + 3 = 9

Both sides are equal.For x = 4:Left hand side: 3 + 2(4) = 3 + 8 = 11

Right hand side: 2(4) + 3 = 8 + 3 = 11

Both sides are equal.For x = 5:Left hand side: 3 + 2(5) = 3 + 10 = 13

Right hand side: 2(5) + 3 = 10 + 3 = 13

Both sides are equal.Hope this helps ðŸ™‚