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1.1. Variables in Algebra. 1. 2. GOAL. GOAL. Evaluate a variable expression. Write a variable expression that models a real-life situation. To express real-life number relationships. What you should learn. Why you should learn it. 1.1. Variables in Algebra.

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1.1

Variables in Algebra

1

2

GOAL

GOAL

Evaluate a variable expression.

Write a variable expression that models a real-life situation.

To express real-life number relationships.

Whatyou should learn

Why you should learn it

1.1

Variables in Algebra

EVALUATING VARIABLE EXPRESSIONS

1

GOAL

• VOCABULARY
• variable
• values
• variable expression
• evaluating an expression

EXAMPLE 1

• To evaluate a variable expression, follow these three steps:
• Write the variable expression.
• Substitutevalues for variables.
• Simplify the numerical expression.

Evaluate each expression when y = 3. Click for solutions.

1. 4y 2. 3. y + 8 4. 18 - y

EXAMPLE 2

Extra Example 1

Solution:

average speed

EXAMPLE 3

Extra Example 2

44.5 mi/h

Find the perimeter, a + b + c, of the triangle. The dimensions are in centimeters.

Click to see the solution.

b = 1.75

a = 1

c = 2.25

Extra Example 3

Perimeter = a + b + c

=

1 + 1.75 + 2.25

=

5 cm

Find the perimeter of the triangle. The dimensions are in inches. Click for the answers.

c = 6.7

a = 8

b = 8

EXAMPLE 4

Checkpoint

1. Find the average speed of a car that travels 225 miles in 4.5 hours.

50 mi/h

22.7 in

Extra Example 4

Find the simple interest, Prt, you will earn in two years on a deposit of \$870 at a rate of 5% per year.

Click for the solution.

Simple interest = Prt

=

Did you remember to

convert the interest rate

to a decimal number?

These units

cancel.

\$87

1.1

Variables in Algebra

2

GOAL

MODELING A REAL-LIFE SITUATION

EXAMPLE 5

• VOCABULARY
• Unit Analysis
• Verbal Model

VERBAL

MODEL

Time

=

LABELS

ALGEBRAIC MODEL

Extra Example 5

You plan to ride your bicycle to school and back at an average rate of 6 miles per hour for a distance of 10.5 miles. How long will it take you? Click to see the solution.

Time = t

Distance = 10.5 miles

Rate = 6 mi/h

1.75 hours

Checkpoint

1. Find the simple interest you will earn after one half of a year with a deposit of \$1250 at a rate of 6% per year.

\$37.50

• Your parents drive to the grocery store 9 miles away at 12:30 p.m. and return at 2:00 p.m. If the grocery shopping took 45 minutes, what was the average speed of their car?