Final answer:
To find the value of m for which the equation 5 – 3x = m + mx has no solutions, we eliminate the m term and set the coefficient of x equal to zero. The value of m that satisfies this condition is 0.
Step-by-step explanation:
To find the value of m for which the equation 5 – 3x = m + mx has no solutions, we need to simplify the equation and analyze it. First, let's eliminate the m term on both sides of the equation:
5 – 3x = m + mx
5 – 3x = m(1 + x)
The equation will have no solutions when the coefficient of x is equal to zero. Therefore, we set the coefficient of x equal to zero and solve for m:
1 + x = 0
x = -1
Substituting x = -1 back into the equation:
m(1 + (-1)) = m(0)
m(0) = 0
So, the equation has no solutions when m = 0.