Question

For what value of m does the equation 5 – 3x = m + mx have no solutions?

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Answer 1

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.