2Cornell Notes HeaderTopic: Inequalities & Two-Step Equations (Unit 7 pg. 1)E. Q.: How are two-step equations applied in the real world?Name: _____________________________Date: _____________________________Class: _____________________________Chp. 10 Lesson 3 (6th grade my.hrw.com) – Two-Step Equations
3Group Question What is the difference between: 3 + 2(6) = x and 10x + 8 = 28In the first equation, the output is unknown. To find the output, you must simplify the left side of the equation using the order of operations.In the second equation, an input is unknown. To find the input, you must work backward and use the reverse order of operations.
4Order and Reverse Order of Operations Please Excuse My Dear Aunt Sallyparentheses, exponents, multiplication & division, addition and subtraction( ), x2, ∙ and ÷, + and –Reverse Order of Operations:- and +, ÷ and ∙, x2, and ( )
5Introduction ProblemMrs. Clark spent forty-three dollars at the grocery store. Eight dollars was spent on vegetables and the rest of the money was spent on five pounds of ribs. How much were the ribs per pound? Write and solve a two step equation to represent the problem.5x + 8 = 43
6Solving Two-Step Equations 1. Undo operations using the reverse of the order of operations.5x + 8 = 43Undo the addition first and then undo the multiplication.2. Check by substituting the value of the variable into the equation to see if it makes a true statement.5(7) + 8 = 4343 = 43 true5x = 35___ ___x = 7
7Solving Two-Step Equations Example undo subtraction first by addingx/ = 149 · x/ = 14 · 9 undo the division by multiplyingx = check: 126/9 - 4 = 10= 1010 = 10
8Solving Two-Step Equations Example Solve: x+7/2 = 30
9Solving Two-Step Equations Example The fraction bar, or division bar, acts as a grouping symbol, like the parentheses.x+7/2 = 30(x+ 7)/2 = 30 add the parentheses2 · (x+ 7)/2 = 30 · 2 undo division first by multiplyingx + 7 = 60undo the addition by subtractingx = 53 check: (53 + 7)/2 = 30
10Function Rules Word Problem The rule for a certain function is to multiply the input by 4 and subtract 3. Find the input value when the output is 33.In the problem we are given the rule and the output and have to find the input for the given output. In order to solve this, we need to work backwards.
11Working Backwards with Function Rules 1. Write an equation for the given function rule.The rule for a certain function is to multiply the input by 4 and subtract 3. Find the input value when the output is 33.4x – 3 = y or y = 4x - 32. Substitute the given output into the equation.4x – 3 = 333. Solve.Undo the subtraction and then undo the multiplication.4. Check answer by substituting the input value into the function rule (equation).4(9) – 3 = 3336 – 3 = or = 334x = 36__ __x = 9
12Group Problem: Working Backwards with Function Rules Derrick has save $40 for go-cart racing. The cost of a racing license is $16, and the cost of each race is $6. How many races can Derrick afford?Cost of a race times # of races cost of license = total cost 6x + 16 = 406x = 24x = 4 races
13SummarySummarize your notes in one to two sentences using the words two-step equations and reverse order of operations.