At what value of a does equation (a-5) x = 3 + 4a have a root equal to -2?

In order to find at what value of the parameter a the equation (a – 5) x = 3 + 4a has a root -2, we will compose and solve an equation with one variable.

Let’s substitute -2 instead of x in the equation and solve the resulting equation for the variable a.

(a – 5) * (-2) = 3 + 4a;

-2a + 10 = 3 + 4a;

We group the terms with and without variables in different parts of the equation.

-2a – 4a = 3 – 10;

Here are similar terms:

a (-2 – 4) = -7;

-6a = -7;

a = -7: (-6);

a = 1 1/6.

The condition of the problem is fulfilled for a = 1 1/6.