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Published byAudrey McIntyre Modified over 4 years ago

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**1.1 What you should learn Why you should learn it Variables in Algebra**

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

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**1.1 Variables in Algebra 1 GOAL EVALUATING VARIABLE EXPRESSIONS**

VOCABULARY variable values variable expression evaluating an expression

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**To evaluate a variable expression, follow these three steps: **

Write the variable expression. Substitute values for variables. Simplify the numerical expression. EXAMPLE 1

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Extra Example 1 Evaluate each expression when y = 3. Click for solutions. 1. 4y y y EXAMPLE 2

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Extra Example 2 Find the average speed, of a car that traveled 89 miles in 2 hours. Solution: average speed 44.5 mi/h EXAMPLE 3

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Extra Example 3 Find the perimeter, a + b + c, of the triangle. The dimensions are in centimeters. Click to see the solution. a = 1 b = 1.75 c = 2.25 Perimeter = a + b + c = = 5 cm

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Checkpoint 1. Find the average speed of a car that travels 225 miles in 4.5 hours. 50 mi/h Find the perimeter of the triangle. The dimensions are in inches. Click for the answers. c = 6.7 a = 8 b = 8 EXAMPLE 4 22.7 in

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**convert the interest rate**

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

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**1.1 Variables in Algebra 2 GOAL MODELING A REAL-LIFE SITUATION**

VOCABULARY Unit Analysis Verbal Model EXAMPLE 5

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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. VERBAL MODEL LABELS ALGEBRAIC MODEL Time = Time = t Distance = 10.5 miles Rate = 6 mi/h 1.75 hours

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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? Click for the answers. 24 mi/h

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QUESTIONS?

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To Start: 20 Points!! -2(4x + 3y – 4z – 11) 12(11) + 12(14) + 12(24) – 12(9) Use front-end estimation: 6.3 + 8.55 Estimate the quotient: 29.5 ÷ 4.83 -8x.

To Start: 20 Points!! -2(4x + 3y – 4z – 11) 12(11) + 12(14) + 12(24) – 12(9) Use front-end estimation: 6.3 + 8.55 Estimate the quotient: 29.5 ÷ 4.83 -8x.

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