Final answer:
To find the value of m for which the equation 5-3x = mx has no solutions, we set the equation equal to 0 and solve for x using the quadratic formula. If the discriminant is negative, there are no solutions. Solving the inequality 9 - 20m < 0 yields m = 9/20.
Step-by-step explanation:
To find the value of m for which the equation 5-3x = mx has no solutions, we need to set the equation equal to 0 and solve for x. This will give us the values of x where the equation is true. If there are no solutions, it means that the equation does not intersect the x-axis. To solve the equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In our equation, a = m, b = -3, and c = 5. Since we want to find the values of m where there are no solutions, we need the discriminant (b^2 - 4ac) to be negative. This means that:
b^2 - 4ac < 0
Substituting the values from our equation, we get:
(-3)^2 - 4m(5) < 0
9 - 20m < 0
To find the values of m where this inequality is true, we solve it as an equation:
9 - 20m = 0
-20m = -9
m = -9/-20
m = 9/20
So, the value of m for which the equation has no solutions is 9/20.