Which equations have no solutions. Mark all that apply.

Question

This problem requires you to show your work.

(2 points)
Responses

7x+3−4x=3(x+1)
7 x plus 3 minus 4 x is equal to 3 times open paren x plus 1 close paren

6(x+8)=6x+5
6 times open paren x plus 8 close paren is equal to 6 x plus 5

2(x+2)=2x+2
2 times open paren x plus 2 close paren is equal to 2 x plus 2

5x+5=5(2x+2)

Answer 1

To solve these equations, we will simplify the equations and check if they are equivalent.

7x + 3 - 4x = 3(x + 1)
Simplifying the equation: 3x + 3 = 3x + 3

No matter what value we substitute for x, both sides of the equation will always be equal. Therefore, this equation has infinitely many solutions.

6(x + 8) = 6x + 5
Simplifying the equation: 6x + 48 = 6x + 5

Subtracting 6x from both sides, we get: 48 = 5

This equation leads to a false statement, indicating that there are no solutions.

2(x + 2) = 2x + 2
Simplifying the equation: 2x + 4 = 2x + 2

Subtracting 2x from both sides, we get: 4 = 2

This equation leads to a false statement, indicating that there are no solutions.

5x + 5 = 5(2x + 2)
Simplifying the equation: 5x + 5 = 10x + 10

Subtracting 5x from both sides, we get: 5 = 5x + 10

Subtracting 10 from both sides, we get: -5 = 5x

Dividing by 5, we get: -1 = x

This equation has a unique solution.

So, the equations that have no solutions are:

6(x + 8) = 6x + 5
2(x + 2) = 2x + 2