Let's solve each equation to determine if it has any solutions:
1) 2(x+2) = 2x + 2
Expanding the left side: 2x + 4 = 2x + 2
Simplifying by subtracting 2x from both sides: 4 = 2
The equation simplifies to 4 = 2, which is not true.
Therefore, this equation has no solutions.
2) 6(x+8) = 6x + 5
Expanding the left side: 6x + 48 = 6x + 5
Simplifying by subtracting 6x from both sides: 48 = 5
The equation simplifies to 48 = 5, which is not true.
Therefore, this equation has no solutions.
3) 7x + 3 - 4x = 3(x+1)
Simplifying the equation: 3x + 3 = 3x + 3
The variable 'x' cancels out on both sides.
The equation simplifies to 3 = 3, which is true.
Therefore, this equation has infinitely many solutions.
4) 5x + 5 = 5(2x + 2)
Expanding the right side: 5x + 5 = 10x + 10
Simplifying by subtracting 10x from both sides: -5x + 5 = 10
Simplifying further by subtracting 5 from both sides: -5x = 5
Dividing by -5 throughout: x = -1
Therefore, this equation has a single solution, x = -1.
Therefore, the equations that have no solutions are:
1) 2(x+2) = 2x + 2
2) 6(x+8) = 6x + 5
Which equations have no solutions. This problem requires you to show your work. (2 points) Responses 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 6 times open paren x plus 8 close paren is equal to 6 x plus 5 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 5x+5=5(2x+2)
1 answer
1 answer