Exercise 19 Page 247

To graph the equation - x-5=- 13(3x+5), we will create two functions out of the left- and right-hand sides of the equation. f(x)=- x-5 and g(x)=-1/3(3x+5) The x-coordinate where the graphs of these functions intersect is the solution to our equation. Since one of the given equations is not in slope-intercept form, let's rewrite it so that it will be easier to identify its slope and y-intercept.

g(x)=-1/3(3x+5)

Distr

Distribute -1/3

g(x)=- x-5/3

Now let's graph these lines.

We can see that the lines are parallel. Therefore, the graphs do not have a point of intersection. We can verify this algebraically by solving the equation.

- x-5=-1/3(3x+5)

Distr

Distribute -1/3

- x-5=- x-5/3

AddEqn

LHS+x=RHS+x

- 5≠-5/3 *

Solving the equation resulted in a contradiction, because - 5 can never be equal to - 53. Therefore, the equation has no solution.