Which equations have no solutions. Mark all that apply.
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
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.