Question

How do you solve `x+2/5=-3/2` by clearing the fractions?

Answer 1

`color(green)(x=-19/10)`
`color(white)("XXX")`see below for solution method by "clearing the fractions"

Explanation:

Given
`color(white)("XXX")color(blue)(x+2/5)=color(blue)(-3/2)`

We can clear the fractions by multiplying both sides by the `color(red)(LCM)` (Least Common Multiple) of all denominators appearing in the equation.

The denominators that we have in the given equation are `color(blue)2` and `color(blue)5`;
their color(red)(LCM) is `color(red)(10)`;
so we will multiply both sides by `color(red)(10)`

`color(white)("XXX")color(red)(10)xx(color(blue)(x+2/5))=color(red)(10)xx(color(blue)(-3/2))`

Simplifying
`color(white)("XXX")10x+4=-15`

`color(white)("XXX")10x=-19`

`color(white)("XXX")x=-19/10`