Question

Solve for the variable: 3.5x=32.2 What’s the variable?

Answer 1

Answer:

The variable is x.

The value of the variable is 9.2.

Step-by-step explanation:

The equation shows the variable x multiplied by 3.5 with the result of that multiplication being 32.2. In order to solve for x, you must "undo" that multiplication.

The definitions of the multiplicative inverse and of the multiplication identity element tell you how to do that. The multiplicative inverse of a number is its reciprocal: the multiplicative inverse of 3.5 is 1/3.5. Multiplying a number by its multiplicative inverse gives a result of 1. Here, that means ...

3.5 × (1/3.5) = 1

The property of the multiplicative identity element (1) is that anything multiplied by that is just that thing:

x · 1 = x

So, to solve this equation, you multiply both sides by the multiplicative inverse of 3.5:

3.5x = 32.2

(1/3.5)(3.5)x = (1/3.5)(32)

1x = 9.2 . . . . . carry out the multiplication

x = 9.2 . . . . . . recognize 1x = x

___

You will recognize that multiplying by 1/3.5 is the same as dividing by 3.5. In other words, we solve this equation by dividing it by the coefficient of x.