Create functions from the left-hand and right-hand sides of the equation.
Number of Solutions: Infinitely many solutions. Solution: All real numbers.
Practice makes perfect
To graph the equation 12(8x+3)=4x+ 32, we will create two functions out of the left- and right-hand sides of the equation.
f(x)=1/2(8x+3) and g(x)=4x+3/2
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.
Solving the equation resulted in an identity, because 32 is always equal to itself. Therefore, the equation is satisfied by all real numbers and has infinitely many solutions.
