Multi-Step Equations with Variables on Both Sides
Multi-Step Equations with Variables on Both Sides - How it Works - Video
Example 1
Example 1:
We have the equation 9x - 5 = 12x - 4. The first step to help is to add the hidden symbols so that we can find the inverse easier. Now we have +9*x - 5 = +12*x - 4. Now we have to get x by itself. You can choose which side you want to move it, but we are going to move the x to the right side since 12 is greater than 9. We must subtract the term -9x from each side since in the equation there is +9x. Now we have -5 = +3*x - 4. We must add the term +4 to each side. Now we have -1 = +3*x. We must divide by the term -3 to both because of the +3 in front of the +3*x. Now we have -1/3 = x and we just flip it to x = -1/3.
Example 2
Example 2:
We have the equation 14x + 7 = 8x + 19. The first step is add the hidden symbols so that we can find the inverse easier. Now we have +14*x + 7 = +8*x + 19. In this case we are moving the x to the left side because 14 is greater than 8 and we will want to have a positive variable. We must subtract the term -8x on both sides to get +6*x + 7 = +19. Now we must subtract the term -7 from both sides because of the +7 on the left side. Now we have +6*x = 12. We must divide each side by the term +6 because of the * next to the +6 and the x. Now we have x = 2.
Example 3a
Example 3a:
We have the equation -2x + 6 = -6x + 14. The first step is add the hidden symbols so that we can find the inverse easier. Now we have -2*x + 6 = -6*x +14. In this case we are moving the x to the left side because -2 is greater than -6 and we will want to have a positive variable. We must add the term +6x to both sides because of the -6x on the right side. Now we have +4*x + 6 = 14. We must subtract the term -6 on both sides because of the +6 on the left side. Now we have +4*x = 8. We must divide each side by +4 because of the * in between +4 and x. Now we have x = 2.
Example 3b
Example 3b:
We have the equation -2x + 6 = -6x + 14. The first step is add the hidden symbols so that we can find the inverse easier. Now we have -2*x + 6 = -6*x +14. In this case we are going to solve it by moving -2x to the other side to show you that equations can be solved multiple ways. We must add the term +2x to both side because of the -2x on the left side. Now we have +6 = -4*x + 14. We must subtract the term -14 from sides because of the term +14 on the right side. Now we have -8 = -4*x. W must divide both sides by -4 because of the * in between -4 and the x. Now we have 2 = x.
As we can see, we get the same as example 3a so it doesn't matter which way you do it.