Question

Consider the equation x−3=5.

a. Multiply both sides of the equation by a constant, and show that the solution set did not change.

Now, multiply both sides by x.

b. Show that x=8 is still a solution to the new equation.

Answer 1

a. Solution did not change

b. x = 8

Explanation:

Solution for the equation is

x−3=5

x = 5 + 3

x = 8

a. Multiply both sides of the equation by a constant, C

C*(x−3) = 5*C

C*x−3*C= 5*C

C*x = 5*C + 3*C

C*x = 8*C

x = 8*C/C

x = 8

b. Multiply both sides of the equation by x

x*(x−3) = 5*x

x^2−3*x= 5*x

x^2 = 5*x + 3*x

x^2 = 8*x

x^2/x = 8

x = 8