Answer:
the value of n that makes the equation have no solution is n = 2.
Explanation:
To find the value of n that makes the equation have no solution, we can start by rearranging the equation in terms of x:
2x + 2 = nx - 3
Let's simplify the equation by combining like terms:
2x + 2 = nx - 3
Moving all the x terms to the left side and the constant terms to the right side, we get:
2x - nx = -3 - 2
Factoring out x on the left side:
x(2 - n) = -5
For this equation to have no solution, the coefficient of x (2 - n) must equal zero. This is because if the coefficient is zero, any value for x would result in the left side of the equation being zero, which would not be equal to the constant term on the right side (-5).
Setting 2 - n = 0, we can solve for n:
2 - n = 0
Subtracting 2 from both sides:
-n = -2
Multiplying both sides by -1 to isolate n:
n = 2
Therefore, the value of n that makes the equation have no solution is n = 2.