Ok so I have this problem, 12x+24=6x+3. WHAT DO I DO IF THE X HAS DIFFERENT NUMBERS. Oh and for 5-2x=2x-5 what do i do if ones a negative and ones a positive. Im trying to find the answer and if its 1 solution, no solution, or infinite solutions. Im sure people on here can reply quicker then my math teacher.

one solution; that solution is x = -7/2 which is the same as x = -3.5

Work Shown:

The idea is to get all the x terms to one side, and the other stuff to the other side. We follow PEMDAS in reverse to help isolate x

12x+24 = 6x+3

12x+24-24 = 6x+3-24 subtract 24 from both sides

12x = 6x-21

12x-6x = 6x-21-6x subtract 6x from both sides

6x = -21 now the x terms are all on one side

6x/6 = -21/6 dividing both sides by 6

x = -21/6

x = (-7*3)/(2*3)

x = -7/2

x = -3.5

This is the only solution. Whenever we have different coefficients for the x terms like this, we can see right off the bat we have exactly one solution. Consider graphing y = 12x+24 and y = 6x+3. The two lines will intersect at the point (x,y) where the x coordinate is the solution to the original equation. There is only one point of intersection which corresponds to exactly one solution.

The thing to notice about y = 12x+24 and y = 6x+3 is that the slopes are not the same, so the lines aren't parallel. Parallel lines always have equal slopes but different y intercepts. If your teacher gave you 12x+24 = 12x+3, then the two lines to graph would be y = 12x+24 and y = 12x+3. At this point, we would get two parallel lines that don't intersect, and therefore we wouldn't get any solutions here.

since both sides equal, there are infinitely many olutions.

16.9 times 2.85

step-by-step explanation: