Question

Which of these equations have no solution? check all that apply.

a)2(x+2) +2 = 2(x +3) +1
b)2x+ 3(x+ 5) = 5(x – 3)
c)4(x+ 3) = x +12
d)4 – (2x +5) = (–4x – 2)
e)5(x+ 4) – x = 4(x +5) – 1

Answer 1

To determine which equations have no solution, we need to solve each equation and see if we end up with a contradiction or false statement. The equations that have no solution are a) 2(x+2) +2 = 2(x +3) +1 and b) 2x+ 3(x+ 5) = 5(x – 3). In these equations, the statement 6 = 7 and 15 = -15 are false, which means that there is no value of x that makes these equations true.

Step-by-step explanation:

To determine which equations have no solution, we need to solve each equation and see if we end up with a contradiction or false statement. Let's go through each equation:

1. a) 2(x+2) +2 = 2(x +3) +1:
   Simplify both sides of the equation:
   2x + 4 + 2 = 2x + 6 + 1
   2x + 6 = 2x + 7
   Subtract 2x from both sides:
   6 = 7
2. b) 2x+ 3(x+ 5) = 5(x – 3):
   Distribute on the left side of the equation:
   2x + 3x + 15 = 5x - 15
   Combine like terms:
   5x + 15 = 5x - 15
   Subtract 5x from both sides:
   15 = -15
3. c) 4(x+ 3) = x +12:
   Distribute on the left side of the equation:
   4x + 12 = x + 12
   Subtract x and 12 from both sides:
   3x = 0
4. d) 4 – (2x +5) = (–4x – 2):
   Distribute the -1 on the right side of the equation:
   4 – 2x – 5 = -4x -2
   Combine like terms:
   -1 – 2x = -4x - 2
   Add 2x to both sides:
   -1 = -2x - 2
   Add 2 to both sides:
   1 = -2x
5. e) 5(x+ 4) – x = 4(x + 5) – 1:
   Distribute on both sides of the equation:
   5x + 20 – x = 4x + 20 – 1
   Combine like terms:
   4x + 20 = 4x + 19
   Subtract 4x from both sides:
   20 = 19

The equations that have no solution are a) and b). In these equations, the statement 6 = 7 and 15 = -15 are false, which means that there is no value of x that makes these equations true.