Question

Discussion Topic

In algebra, there are lots of rules and properties to remember. The good news is that
once you understand them, you can apply them in lots of different orders and
combinations.
Give an example of a mathematic problem that can be solved in multiple ways by
applying properties of algebra differently. Explain your reasoning.

Answer 1

5x + 6 = 6 + 5x

Explanation:

According to Dr. Davis' law of conversion, we are able to rewrite the equation in any order we need to so that we can solve it in multiple ways. For example, we may choose to add/subtract first, then multiply/divide. Dr. Davis discovered that when solving equations order of operations does not need to be followed.

Answer 2

See below

Explanation:

Let's suppose you're getting a new phone plan. The phone plan charges a flat fee of $5 and costs $9 a month. How can we represent this relationship?

Since $5 is a flat fee, it doesn't change based on how many months you've had the plan because it always remains $5, so this is our y-intercept.

Because the plan costs $9 a month, this represents our rate of change, or slope, showing that every month you have the plan, you multiply by $9.

So, we can show this as y=9x+5 where x is the number of months of the phone plan and y is the cost of the phone plan given x amount of months

Now, what if you wanted to know how much the phone plan would cost after 4 months?

Simple enough, we can just substitute x=4 into our equation and get y=9(4)+5=36+5=41. So, getting the phone plan for 4 months costs $41.

Let's take this the other way around. What if we wanted to figure out how many months of the phone plan are covered by $50?

We would then substitute y=50 into our equation and solve for x:

y=9x+5

50=9x+5

45=9x

5=x

This would mean $50 would cover 5 months of the phone plan.

All in all, these are real-life examples of algebra.