Question 85331
{{{10(-x - 7) + 20 = -5(2x + 4)}}} Start with the given equation


{{{-10*x - 10*7 + 20 = -5*2x + -5*4)}}} Distribute



{{{-10x - 70 + 20 = -10x + -20)}}} Multiply


{{{-10x +10x - 70 + 20 = cross(-10x +10x) + -20)}}} Add 10x to both sides


{{{-70+20=-20}}} Notice the x terms add to zero


{{{-50=-20}}} Combine like terms


Since this equation is false no matter what x is equal to (x is not a factor in this equation any more), there are no solutions. Notice if we graph the equations

{{{y=10(-x - 7) + 20}}} here is the left equation in y form

{{{y=-5(2x + 4)}}} here is the right equation in y form


we get


{{{ graph( 300, 200, -6, 5, -10, 10, 10(-x - 7) + 20,-5(2x + 4)) }}}


and here you can clearly see that these two parallel lines will never intersect. Since they never intersect, there are no solutions.