Question

Please explain your answer to the question in the picture with steps

Answer 1

x = 31.2

Explanation:

You want the solution to the proportion 12/x = 5/13.

Rational equation

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

`(12)/(x)*13x=(5)/(13)*13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}`

Now, the value of x is found by dividing both sides by its coefficient.

`(12\cdot13)/(5)=(5x)/(5)\\\\\\(156)/(5)=x\\\\\boxed{31.2=x}`

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Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

`(12)/(x)=(5)/(13)\qquad(x)/(12)=(13)/(5)\qquad(x)/(13)=(12)/(5)\qquad(13)/(x)=(5)/(12)`

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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