How many solutions will the equation 5(3x - 9) = 2(6x + 9) have and please explain?

Answer 1

This problem will have 1 solution.

The best way to do this type of problem is to expand everything to make it easier to solve.

5(3x - 9) = 2(6x +9) ----We will distribute the 2 and 5

15x - 45 = 12x + 18 -----Now we will move the x's to one side

15x - 12x = 18+ 45 -----Simplify

3x = 63 ----Divide both sides by 3

x = 21.

This is the only solution.

Answer 2

15x-45 = 12x + 18

3x = 63

x = 21

just one solution

You could treat this as 2 lines, y=15x-45 and y=12x + 18, then when x=21, y= 252+18= 270

the point (21,270) is the point of intersection of the 2 lines, and the unique sole solution to the 2 equations