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**

Be sure to check out the youtube video:

**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.**

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