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1.1 Variables in Algebra What you should learn 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. 1.1 Variables in Algebra GOAL 1 EVALUATING VARIABLE EXPRESSIONS VOCABULARY •variable •values •variable expression •evaluating an expression To evaluate a variable expression, follow these three steps: •Write the variable expression. •Substitute values for variables. •Simplify the numerical expression. EXAMPLE 1 Extra Example 1 Evaluate each expression when y = 3. Click for solutions. 1. 4y 4(3) 12 2. 12 y 12 3 4 EXAMPLE 2 3. y + 8 4. 18 - y 38 11 18 3 15 Extra Example 2 d Find the average speed, , of a car that traveled 89 miles in t 2 hours. Solution: d average speed t 89 miles 2 hours 44.5 mi/h EXAMPLE 3 Extra Example 3 Find the perimeter, a + b + c, of the triangle. The dimensions are in centimeters. b = 1.75 Click to see the solution. a=1 c = 2.25 Perimeter = a + b + c = 1 + 1.75 + 2.25 = 5 cm Checkpoint 1. Find the average speed of a car that travels 225 miles in 4.5 hours. 50 mi/h 2. Find the perimeter of the triangle. The dimensions are in inches. Click for the answers. c = 6.7 a=8 EXAMPLE 4 b=8 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? 0.05 (2 years) = ($870) year = $87 These units cancel. 1.1 Variables in Algebra GOAL 2 MODELING A REAL-LIFE SITUATION VOCABULARY •Unit Analysis •Verbal Model EXAMPLE 5 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 Distance = Rate Time = t Distance = 10.5 miles Rate = 6 mi/h 10.5 miles t 6 mi/h 1.75 hours mi mi/h mi h h mi 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 2. 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? 24 mi/h Click for the answers. QUESTIONS?