Question

Which of these equations have no solution? Check all thal apply.

2(x + 2) + 2 = 2(x + 3) + 1
2x + 3(x + 5) = 5(x - 3)
46x + 3) = x + 12
4- (2x + 5) = 2 ( 4x - 2)
5(x + 4) - x = 4(x + 5) - 1
​

Answer 1

A, B, E

Explanation:

Answer 2

2(x + 2) + 2 = 2(x + 3) + 1

2x + 3(x + 5) = 5(x - 3)

5(x + 4) - x = 4(x + 5) - 1

Explanation:

`2(x+2)+2=2(x+3)+1\qquad\text{use the distributive property}\\2x+4+2=2x+6+1\qquad\text{subtract 2x from both sides}\\6=7\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\2x+3(x+5)=5(x-3)\qquad\text{use the distributive property}\\2x+3x+15=5x-15\\5x+15=5x-15\qquad\text{subtract 5x from both sides}\\15=-15\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\46x+3=x+12\qquad\text{subtract x from both sides}\\45x+3=12\qquad\text{subtract 3 from both sides}\\45x=9\qquad\text{divide both sides by 45}\\x=(9)/(45)\to x=(1)/(5)\to\text{one solution}\\===============================\\4-(2x+5)=2(4x-2)\qquad\text{use the distributive property}\\4-2x-5=8x-4\\-2x-1=8x-4\qquad\text{subtract 8x from both sides}\\-10x-1=-4\qquad\text{add 1 to both sides}\\-10x=-3\qquad\text{divide both sides by (-10)}\\x=0.3\to\text{one solution}\\===============================\\5(x+4)-x=4(x+5)-1\qquad\text{use the distributive property}\\5x+20-x=4x+20-1\\4x+20=4x+19\qquad\text{subtract 4x from both sides}\\20=19\qquad\boxed{FALSE}\to\text{no solution}`