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

Solve the equation 3(5+2x)=8(5+x) for x.

Summary

  1. 'x' is a variable
  2. To 'solve for x' you need to get 'x' by itself on one side of the equation
  3. To check the answer, plug it into the original equation and simplify

Notes

    1. Distributing the 3 means that you multiply each term inside the parentheses by 3
    1. Distributing the 8 means that you multiply each term inside the parentheses by 8
    1. 'x' is the variable we're trying to solve for
    2. To solve for 'x', we need to get it by itself on one side of the equation
    3. So since right now we have x's on both sides, we need to move them both to the same side
    1. 'x' is a variable
    2. Subtracting '8x' from both sides of the equation cancels the '8x' on the right
    3. On the left 6x-8x is equal to -2x
    4. So now all the 'x' terms are on the left
    1. 'Isolate x' means we want to get 'x' by itself on one side
    2. Remember, 'x' is the variable we're trying to solve for
    3. In order to do this, we need to move everything that DOESN'T have an 'x' to the right hand side
    1. 'x' is a variable
    2. Subtracting '15' from both sides of the equation cancels the '15' on the left
    3. On the right 40-15 is equal to 25
    1. Dividing by '-2' will get the 'x' all by itself on the left hand side
    2. We need to make sure we divide by NEGATIVE 2, not just 2, since we want to find 'x', not '-x'
    1. If you divide by '2' instead of '-2', you'd end up with a '-x' instead of an 'x'
    2. To solve for 'x', you need to get 'x' completely by itself, and a -x has a -1 in front of it
    1. To check our answer, we want to plug what we got for x (-25/2) into the original equation to see if we get a true statement
    2. If we do, then our answer is correct!
    1. Multiply what's inside the most inner parentheses first, so multiply 2•(-25/2) to get -25
    2. We can rewrite 5 as 10/2 on the right so that we have a common denominator and can subtract the fractions
    3. We still have some parentheses, so subtract inside each of those to get -20 on the left and -15/2 on the right
    4. Then you can multiply to get -60 on each side
    5. Since -60 does in fact equal -60, we know our answer is correct!