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Math Moment – Automotive Technologies HS.A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Materials Note-taker Worksheet Automotive Technologies HS.A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters AKA Solving equations and inequalities Bellwork Think about the many ways of communicating. Write 2 on your note-taker Share with your partner. Math Check What is the difference between and equation and an inequality? Identify if the symbol is for an equation or an inequality. = > Math Check Inverse operations – an operation that undoes another operation. Inverse operations + and – and Steps for solving equations and inequalities 1. ◦ ◦ Simplify each side of the equation or inequality Use the distributive property Combine like terms Move variables to one side and the numbers to the other 3. Use inverse operations to undo addition/subtraction 4. Use inverse operations to undo multiplication/division 2. Be careful The steps in solving equations and inequalities are the same UNLESS you multiply or divide by a negative. If you do multiply or divide by a negative the direction of the inequality reverses or flips. Why does it reverse? We need to stay true to arithmetic Example 3 6 is a true statement What it looks like in math! Solve 1. 3x 7 11 2. 5b 9 4 4 3. 4. 5 y 1 y 7 x 9 51 You try! 1. 2. 9 x 6 24 40 28 x 138 Auto Example A replacement part for Cara’s automobile costs $22.50. The mechanic charges $25 per hour for making the repair. How many hours could the repair take if the total bill is under $100.00? x = hours $22.50 25 x $100.00 You try! The Ace Garage assesses a $15 “shop charge” plus $20 an hour for labor. How many hours of labor did a repair take if the total charge was less than $85? x = hours $15.00 20 x $85.00 Two Estimates Professor Kleinwort receives two estimates for the repair of his antique sedan. The first shop will charge $595 for parts plus $22.50 per hour for labor. A second shop offers to repair the car for $700 plus $19 per hour for labor. How many hours of labor must be involved in order to make the second estimate the cheaper? x = hours $595 $22.50 x $700 $19 x 3-MINUTE CLOSURE OUTCOME STATEMENTS I need more help with . . . PROPERTY OF AZ CTE CURRICULUM CONSORTIUM, 2013