www.VirtualNerd.com

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

Solve 3/2 + 3x/5 = 9/2 + 4x/5 for x

Summary

  1. Multiply by 10 to get rid of the fractions
  2. The two 6x's cancel out on the left, and 8x minus 6x is 2x
  3. The 45's cancel out on the right hand side, and 15 minus 45 is -30
  4. -30 divided by 2 is -15
  5. We now know 'x = -15'
  6. Check the answer by plugging it into the original equation, and evaluating the result
  7. Subtract the whole numbers 9 and 12 from the fractions

Notes

    1. 10 is the smallest multiple of both 2 and 5
    1. LCD stands for least common denominator
    2. The LCD for our fractions is 10
    1. 10 is the least common denominator of our fractions
    2. 'x' is a variable
    1. Multiply 10 by the fractions inside the parentheses
    1. Multiply 10 by each fractions inside the parentheses
    2. 'x' is a variable
    1. Simplify the first term on the left hand side to get 15
    1. 'x' is a variable
    2. Simplify the second term on the left hand side to get 6x
    1. Simplify the first term on the right hand side to get 45
    1. 'x' is a variable
    2. Simplify the second term on the right hand side 8x
    1. 'x' is a variable
    2. Get 'x' on one side, and by itself
    1. Subtraction is the opposite of addition
    2. 'x' is a variable
    1. Subtract 6x from both sides of the equation
    2. 'x' is a variable
    3. The left hand side is 15
    4. The right hand side is 45 plus 2x
    1. Subtraction is the opposite of addition
    1. Subtract 45 and simplify both sides
    2. 'x' is a variable
    3. The left hand side is -30
    4. The right hand side is 2x
    1. Division is the opposite of multiplication
    1. 'x' is a variable
    2. Divide by 2 and simplify
    3. The left hand side is -15
    4. The right hand side is just 'x'
    1. Plug our answer, -15, in for 'x' in the original equation
    2. If the original equation froms a true statement with 'x = -15' then we know how answer is correct
    3. 'x' is a variable
    1. 'x' is a variable
    2. Anywhere you see an 'x' in the original equation, put a -15 instead
    1. The left hand side is now 3 over 2 plus -45 over 5
    2. The right hand side is now 9 over 2 plus -60 over 5
    1. Lets keep simplifying
    2. The left hand side is now 3 over 2 minus 9
    3. The right hand side is now 9 over 2 minus 12
    1. If we get everything over a common denominator of 2, we can subtract our numbers
    1. If we get everything over a common denominator of 2, we can subtract our numbers
    1. Subtract the numerators on the left side, 3 - 18 = -15
    2. Then subtract the numerators on the right side, 9 - 24 = -15