Which equations have no solutions. Mark all that apply.

Question

This problem requires you to show your work.

(2 points)
Responses

5x+5=5(2x+2)
5 x plus 5 is equal to 5 times open paren 2 x plus 2 close paren

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

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

6(x+8)=6x+5

Answer 1

To solve each equation, start by simplifying both sides of the equation.

1) 5x + 5 = 5(2x + 2)
Distribute the 5 on the right side: 5x + 5 = 10x + 10
Subtract 5x from both sides: 5 = 5x + 10
Subtract 10 from both sides: -5 = 5x

The equation -5 = 5x has a solution: x = -1

2) 7x + 3 - 4x = 3(x + 1)
Simplify the left side: 3x + 3 = 3(x + 1)
Distribute the 3 on the right side: 3x + 3 = 3x + 3
Subtract 3x from both sides: 3 = 3

The equation 3 = 3 has infinitely many solutions.

3) 2(x + 2) = 2x + 2
Simplify both sides: 2x + 4 = 2x + 2
Subtract 2x from both sides: 4 = 2

The equation 4 = 2 has no solution.

4) 6(x + 8) = 6x + 5
Simplify both sides: 6x + 48 = 6x + 5
Subtract 6x from both sides: 48 = 5

The equation 48 = 5 has no solution.

Therefore, the equations that have no solutions are 4) 2(x+2)=2x+2 and 5) 6(x+8)=6x+5.