Concepts of Algebra | Linear Equations | Properties of Equality

Before discussing Linear Equations, let's review what an equation is.

So here’s a scenario: I want to throw my brother a party. The venue that I’m renting will cost $500 for the day and there is a $22 per person fee for the foodservice.

Alright so if the variable x represents the number of people in attendance.

The total cost of the party can be represented by the expression,

500 +22x

“500 plus 22 times the number of people in attendance”

If my budget is $2700, then equivalently the cost can be represented by the expression,

500+22x=2700

Now, what is the solution, the root? What value of x satisfies this equation. We need to isolate x, move everything else to the right-hand side of the equal sign and still keep the expression equivalent.

Here's a review of the properties of equality

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So back to the scenario:

If my budget is $2700, then equivalently the cost can be represented by the expression,

If my budget is $2700, then equivalently the cost can be represented by the expression,

500+22x=2700

Let's solve for the variable x and see how many people at most can be in attendance.

Given:

500+22x=2700

500 - 500 + 22x = 2700 - 500

[ Subtraction Property of Equality]

22x=2200

22x/22=2200/22

[Division Property of Equality]

x=100

So the most people in attendance can be 100.