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How Do You Solve an Equation with Variables on Both Sides?

Solve 15 + 6x = 45 + 8x for x

Summary

  1. 'x' is our variable
  2. We have x's on both sides of the equation
  3. Subtract 6x from both sides to get all the x's on one side
  4. Subtract 45 from both sides to get the x term by itself
  5. Divide by 2 on both sides to solve for x
  6. We get x=-15
  7. Plug -15 in for x in the original equation
  8. Since -75=-75 is a true statement, our answer is correct

Notes

    1. 'x' is a variable
    1. 'x' is a variable
    1. 'x' is our variable
    1. 'x' is our variable
    2. The opposite of addition is subtraction
    3. So we need to subtract 6x from both sides of the equation
    1. 'x' is our variable
    2. We have 15+6x-6x on the left hand side
    3. The 6x's cancel out, leaving us with 15
    4. Then we have 45+8x-6x on the right hand side
    5. Subtract 8x-6x and we're left with 45+2x on the right hand side
    1. 15-45 gives us -30 on the left hand side
    2. 45-45+2x leaves us with 2x on the right hand side
    1. 'x' is our variable
    2. Now we have x by itself on one side of the equation
    1. 'x' is our variable
    1. 'x' is our variable
    1. Division is the opposite of multiplication
    2. So divide -30 by 2 and 2x by 2
    1. 'x' is our variable
    2. -30/2=-15
    3. 2x/2=x
    1. -15 is the value we got for our variable, x
    2. So we can plug -15 in wherever we had an x in our original equation
    1. -15 is the value we got for our variable, x
    2. So we can plug -15 in wherever we had an x in our original equation
    1. If we get a true statement, then our answer is correct
    1. -15 was the value we plugged in for x
    1. 15+(-90)=-75
    2. 45+(-120)=-75
    3. Since -75=-75, we get a true statement
    1. So -15, the value we found for x, is the correct answer!