Objectives Use variables to represent

unknown quantities. Represent real-world situations

with equations and solve by guess-and-check.

1.2 Variables, Expressions, and Equations

Page 11

Glossary Terms

Variable – letters used to represent unknown quantities

algebraic expression - combining numbers and variables using addition, subtraction, multiplication and division

Equation – two expressions connected by an equal sign

solution to an equation – all values of the variable that make the equation true

At City Park you can rent in-line skates and protective gear for $2 per hour plus a $4 fee. Write an expression that represents the cost of renting skates and then write an equation that relates the expression to a total cost of $10.

Number of Hours Expression for cost

1 4 + 2(1)

2 4 + 2(2)

3 4 + 2(3)

The rental cost is 4 + 2 times the # of hours

4 + 2h

If the total cost of renting the skates is $10, the equation relating the expression to the cost is : 4 + 2h = 10

When one side of an equation has the same value as the other side, the equation is said to be true.

To determine whether an equation is true or not simplify both sides of the equation.

4 + 2(3) = 6 + 2(2)4 + 6 = 6 + 4

10 = 10

The left and right sides of the equation have the same

value, therefore the equation is true.

Remember, the solution to an equation is the value(s) of the variable that makes

the equation true.

Jessica places 3 photos on the cover of her photo album. She places 4 photos on each of the other pages. She has 155 photos in all. How many pages will she need if she uses

all her photos?

Let p equal the number of pages in the photo album. So the equation will be 4p + 3 = 155

Use guess and check to solve

Try p = 204(20) + 3 = 155

80 + 3 = 15583 = 155Too low.

Try p = 404(40) + 3 = 155160 + 3 = 155

163 = 155Too high.Try p = 38

4(38) + 3 = 155152 + 3 = 155

155 = 155So she needs 38 pages

Key Skills

Evaluate expressions for given values of the variable.

1.2 Variables, Expressions, and Equations

Evaluate 5x – 7 for x = 2 and x = 6.

Evaluate for x = 2 Evaluate for x = 6

5(2) – 7 5(6) – 7

10 – 7 30 – 7

3 23

Key Skills

Write an equation to represent a problem situation.

Membership in a gym at a community center costs $15 per month plus a one-time fee of $50.

Write an equation for the total cost, c, for membership over m months.

The cost is $50 plus $15 every month.c = 50 + 15m

TOC

Page 16 – 17 # 10 – 30 even, 31 – 39, 44 – 48

When you get to 44 – 48 you will have to THINK!!!!

Assignment