Solving symbolic equations

Example 01

Solve equation

and

. Solution. To solve the equation by

, we multiply both sides of the equation by

To solve the equation by

, we need a few steps:

Alternatively, we may solve the equation as a proportion equation, by writing

Solve equation

and

. Solution. First, let us solve the equation by

Then we solve the equation by

The height of a baseball during a throwing motion is given by the equation

Here

is the height during a given time

, while

is the initial height (i.e. height at the beginning),

is the initial velocity, and

is the gravitational acceleration,

. Let

and

. We calculate when the baseball hits the ground. At ground level,

, so we can write:

So according to the zero product property, either

(this is the time when the baseball is thrown in the air), or

Now we can calculate the value for