Multi-Step Equations with Variables on Both Sides - How to Solve Them

Multi-Step Equations with the Distributive Property - How it Works - Video

Example 1

Example 1:

To solve for the x, we must distributive the number and the symbol in front of the parenthesis to each term inside the parenthesis. After adding the hidden symbols (the positive signs and the dot for multiplication), we can see what operation or inverse step that we need to do.

We distribute the +4 to the +3*x to get +12*x and +4 to the +6 to get +24. So now we have +12*x+24.

We distribute the -2 to the +4*x to get -8*x and -2 to the -3 to get +6. So now we have -8*x+6. After we combine, we have

+12*x + 24 - 8*x + 6 = +14. After changing the terms around, so the like terms are closer together, we have +12*x - 8*x + 24 + 6 = +14.

Now we add +12*x - 8*x = +4*x and add +24 + 6 = +30. This gives us +4*x + 30 = +14. We have combined all like terms on each side so now we can find the inverses to isolate x. The inverse of addition is subtraction so subtract the term, 30, on both sides to get +4*x = -16. Finally we divide by the number in front of the variable, x, on both sides, and that is +4. After dividing, we get +1*x = -4. We can drop the symbol and the 1 to get the result of x = -4 as the answer.

Example 2

Example 2:

To solve for the x, we must distributive the number and the symbol in front of the parenthesis to each term inside the parenthesis. After adding the hidden symbols (the positive signs and the dot for multiplication), we can see what operation or inverse step that we need to do.

We distribute the -2 to the +2*x to get -4*x and -2 to the -6 to get +12. So now we have -4*x+12.

We distribute the +3 to the +4*x to get 12*x and +3 to the -5 to get -15. So now we have +12*x-15. After we combine, we have

-4*x + 12 + 12*x - 15 = +21. After changing the terms around, so the like terms are closer together, we have -4*x + 12*x + 12 - 15 = +21.

Now we add -4*x + 12*x = +8*x and add +12 - 15 = -3. This gives us +8*x - 3= +21. We have combined all like terms on each side so now we can find the inverses to isolate x. The inverse of addition is subtraction so add the term, 3, on both sides to get +8*x = +24. Finally we divide by the number in front of the variable, x, on both sides, and that is +8. After dividing, we get +1*x = 3. We can drop the symbol and the 1 to get the result of x = 3 as the answer.

Example 3

Example 3a:

To solve for the x, we must distributive the number and the symbol in front of the parenthesis to each term inside the parenthesis. After adding the hidden symbols (the positive signs and the dot for multiplication), we can see what operation or inverse step that we need to do. In this case, we have to distribute on both sides, but it is the same steps.

We distribute the -1 to the +2*x to get -1*x and -1 to the -6 to get +6. So now we have -2*x+6.

We distribute the +3 to the +7*x to get +21*x and +3 to the -1 to get -3. So now we have +21*x-3. After we combine, we have

-2*x + 6 + 6 = +21*x - 3. This time we have variables on both sides so we need to find the inverse a bit earlier than before. Before that we combine +6 + 6 on the left side to get -2*x + 12 = +21*x - 3. Now we are going to move the variable x on the right side because +21 is greater than -2. We do this because the variable will be positive. Now we add the term +2*x to both sides to get 12 = +21*x + 2*x - 3 then 12 = +23*x - 3. Now we add the term +3 to both sides since addition is the inverse of subtraction. Now we get +12 + 3 = +23*x then +15 = +23*x. Now divide by the number in front the variable, x to both sides since the operation between +23 and x is multiplication. For our final result, we get x = 15/23

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