# Unit 7: Two-Step Equations and Inequalities

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Unit 7: Two-Step Equations and Inequalities
Lesson 1 – Two-Step Equations

Cornell Notes Header Topic: 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

Group Question What is the difference between:
3 + 2(6) = x and 10x + 8 = 28 In 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.

Order and Reverse Order of Operations
Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication & division, addition and subtraction ( ), x2, ∙ and ÷, + and – Reverse Order of Operations: - and +, ÷ and ∙, x2, and ( )

Introduction Problem Mrs. 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

Solving Two-Step Equations
1. Undo operations using the reverse of the order of operations. 5x + 8 = 43 Undo 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 = 43 43 = 43 true 5x = 35 ___ ___ x = 7

Solving Two-Step Equations Example
undo subtraction first by adding x/ = 14 9 · x/ = 14 · 9 undo the division by multiplying x = check: 126/9 - 4 = 10 = 10 10 = 10

Solving Two-Step Equations Example
Solve: x+7/2 = 30

Solving 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 parentheses 2 · (x+ 7)/2 = 30 · 2 undo division first by multiplying x + 7 = 60 undo the addition by subtracting x = 53 check: (53 + 7)/2 = 30

Function 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.

Working 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 - 3 2. Substitute the given output into the equation. 4x – 3 = 33 3. 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 = 33 36 – 3 = or = 33 4x = 36 __ __ x = 9

Group 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 = 40 6x = 24 x = 4 races

Summary Summarize your notes in one to two sentences using the words two-step equations and reverse order of operations.