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Mastering Multi-Step Equations and Inequalities: A Comprehensive Guide

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6 diapositives · 195 Views · Sep 29, 2014

This guide provides a thorough exploration of solving multi-step equations and inequalities with rational coefficients. Students will learn to tackle problems numerically, algebraically, and graphically, using and without technology. Key concepts include translating word problems into equations, understanding equalities, and applying methods through practical examples. From age-related problems to distance-speed equations, this resource equips students with the skills to formulate and solve complex mathematical scenarios effectively.

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Mastering Multi-Step Equations and Inequalities: A Comprehensive Guide
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  1. Solving Written Problems SEI.3.AC.1SLE 1: Solve, with and without appropriate technology, multi-step equations and inequalities with rational coefficients numerically, algebraically and graphically Students will be able to write the equations to solve problems.

  2. Simple Problems • Multiply a number by 3 and you get 15. Find the number. • What will our variable represent? • Let’s translate into symbols the sentence a number “Multiply by 3 a number and you get 15.” 3· x 15 = Equations and Inequalities

  3. Equal sign? • What words or phrases would mean equal? • Here are some examples equals is equal to is or are was or were will be and you get Equations and Inequalities

  4. Example 1 Solve this problem: In 5 years, Linda will be 20 years old. How old is she now? • What will our variable represent? Linda’s age now • How old will Linda be in 5 years x + 5 • So now our equation would be: x + 5 = 20 Equations and Inequalities

  5. Examples 2 Diane drove 240 miles in 4 hours. What is her rate of speed? • What will our variable represent? Her rate of speed • What formula should we use to set up the equation? rate x time = distance • What is the equation? 4 · x = 240 Equations and Inequalities

  6. Examples 3 Two more than 3 times a number is 4 less than 2 times the number. • What would be the variable? Where will the = go? the number • Translate “2 more than 3 times a number” 3x + 2 • Translate “4 less than 2 times the number” 2x – 4 • What is the equation? 3x + 2 = 2x - 4 Equations and Inequalities