Answer:
Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution.
Explanation:
We are looking at two lines.
4(x + 3) + 2x = 6(x +2)
4x + 12 + 2x = 6x + 12
6x + 12 = 6x + 12
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
4x + 11 = 4x + 3
Both lines have the same gradient but have a different incline with the y axis. By definition, they are parallel to each other and there fore have zero solutions. Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution, which is the answer we are looking for.
5(x + 3) + x = 4(x +3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 15
These are two different lines with exactly one solution.
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
6x + 16 = 6x + 16
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).