Question

Solve the following equations without the use of a model. Write all fractional answers in simplest form. Be sure to check your solutions.

Answer 1

So,

We're going to solve the following equation:

`(7)/(2)p-(11)/(12)=(5)/(9)`

The first thing we need to do, is to pass all the numbers (independent terms) to the other side of the equation, and let the variable p in the other side.

Notice that if we pass the numbers to the other side, they will pass with the opposite sign. Like this:

`(7)/(2)p=(11)/(12)+(5)/(9)`

Now we're going to sum the fractions:

`\begin{gathered} (7)/(2)p=(99+60)/(108) \\ \\ (7)/(2)p=(159)/(108) \end{gathered}`

Now, we just multiply the denominator to the other side, and divide by the numerator:

`p=(159\cdot2)/(108\cdot7)=(318)/(756)`

Simplifying, we got that:

`p=(53)/(126)`

Example:

Suppose you have the equation:

`x-1=2`

We are looking for let the variable "x" alone in a side of the equation, so, to do this we could sum "1" to both sides:

`\begin{gathered} x-1+1=2+1 \\ x=3 \end{gathered}`

The same thing happens in this problem.