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2 1/2x-2 1/4=3 2/5

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Hi Kaitlin, First we need to make the problem clear. A good way is to use parentheses ( ) to group terms. So is your problem:  (2 1/2)(x) - (2 1/4) = (3 2/5) ?

Assuming that is what you mean, get all the terms that do NOT have x all together on one side of the =, and leave only the term with x on the other side.  We do that by adding/subtracting the terms we don't want from both sides of the equation ("whatever you do to one side, you must also do to the other, to keep it equal")

(2 1/2)(x) - (2 1/4) + (2 1/4) = (3 2/5) + (2 1/4)

(2 1/2)(x) = (3 2/5) + (2 1/4) = 113/20  (changed 3 2/5 to 17/5, and 2 1/4 to 9/4, then used a common denominator of 5*4 = 20, so 17/5 = 68/20, and 9/4 = 45/20:  68/20 _ 45/20 = 113/20)

 

For the x-term on the left, let's make it a simple fraction:  1 1/2 = 5/2, and (5/2)(x) = 5x/2

Now we have 5x/2 = 113/20

Multiply both sides of the = by 2 to get 5x alone:  (5x/2)(2) = (113/20)(2)

5x = 226/20

Now divide both sides by 5 to get x alone:  5x/5 = (226/20) / 5

x = 226/100, or x = 2.26, or x = 2 26/100, or x = 2 13/50