Exercise 17 Page 247

To graph the equation - 4(2-x)=4x-8 we will create two functions out of the left- and right-hand sides of the equation. f(x)=- 4(2-x) and g(x)=4x-8. 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.

f(x)=- 4(2-x)

Distr

Distribute (- 4)

f(x)=- 8+4x

CommutativePropAdd

Commutative Property of Addition

f(x)=4x-8

Now let's graph these lines.

The graphs are identical which means the functions have infinitely many solutions. We can verify this algebraically by solving the equation.

- 4(2-x)=4x-8

Distr

Distribute - 4

- 8+4x=4x-8

AddEqn

LHS+8=RHS+8

4x=4x

SubEqn

LHS-4x=RHS-4x

0=0 ✓

Solving the given equation resulted in an identity, because 0 is always equal to 0. Therefore, the equation has infinitely many solutions.