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what is x for: 7/3 * x = 4/5

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2 Answers

Fist step, as always with equations is:

1. determine what is happening to the variable, in this case the x.

2. It appears the x (on the left side) is being multiplied by the fraction 7/3.

3. we want x by itself on the left so we need to get rid of the 7/3.  Since x is being multiplied by 7/3 we must divide both sides of the equation by the same amount; 7/3.

4. 7/3x divided by 7/3 equals x all alone.  Ok the left side is done.

5. Now we divide 4/5 by 7/3.  This is done by flipping our 7/3 to its reciprocal of 3/7.  Then we multiply the flipped fraction and the 4/5.  You should get 12 (3*4) over 35 (5*7) or 12/35.  This cant be reduced so we are done!

The idea is to divide both sides by the coefficient of x, which is 7/3. Note that dividing by a fraction is the same as multiplying by its reciprocal.

(7/3)x = 4/5

x = (4/5) / (7/3)      divide by 7/3

x = (4/5) * (3/7)     the reciprocal of 7/3 is 3/7

x = (4*3) / (5*7)    multiplication of fractions -->  a/b * c/d = ac / bd.

x = 12/35               simplification