Lesson 6: Creating Single Variable Equations and Inequalities A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential factors. SWBAT create a single variable equation

EQUATIONS AND INEQUALITIES are used to represent a quantity that we want to end up with and the parts that we combine to get it.

Important Vocabulary Equation: a mathematical sentence that uses an equal sign (=) to show that two quantities are equal Inequality: a mathematical sentence that shows the relationship between quantities (That one quantity is either greater than or less than the other) Quantity: something that can be compared by assigning a numerical value Solution: a value that makes the equation true Variable: a letter used to represent a value or unknown quantity that can change or vary

Equations/Inequalities 1. Five times the sum of a number and two is thirty-five. 2. Twelve subtracted from three times a number is less than fifteen. 3. Twice a number added to seven is greater than thirteen. 4. The sum of a number added to it self is at least 126. 5. When 6 is added to four times a number, the result is 50.

Example 1 You are trying to save $20 a week to buy a new CD player. During the last 4 weeks you have saved $35, $15, $10, and $12. How much do you need to save this week to average $20 for the 5 weeks?

Example 2 On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138.

Example 3 Brianna has saved $600 to buy a new TV. The TV she wants costs $1,800 and she saves $20 a week. Write an equation that represents the how the money she makes and has saved can combine to the cost of the TV.

Guided Practice 1. JaQuandon has 5 of the newest mixtapes from Datpiff.com. Regis has 3 less than twice the number of mixtapes that JaQuandon has. Write an equation the demonstrates the relationship between the number of mixtapes JaQuandon and Regis have.

Guided Practice 2 The width of a rectangle is 8 inches more than the length. The perimeter is 32.

Guided Practice 3 The sum of 3 consecutive integers is 159. After creating the equation, can you find the 3 numbers?

Independent Practice

Ticket out the Door Six time the difference of 5 times a number and 10. Jenny has 4 more than twice as much as cookies as Carry.

Lesson 6 part 2 A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential factors. SWBAT create a single variable inequality

Inequalities Less than < Less than or equal to ≤ Greater than > Greater than or equal to ≥ Fewer than Below Less than Smaller than No more than Not above Does not exceed At most Maximum More than Exceeding Above Bigger than At least No fewer than Not under No less than Minimum

Quick Check! 1. A number is no more than 5   2. Clark has at least 8 hats 3. Marcus exceeded his saving of $200 4. Tony borrowed fewer than 30 pencils

Example 1 Antara has $500 in a savings account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week.

Example 2 Keisha charges a $1.75 flat rate to braid hair in addition to $0.65 per braid. Lanoria has no more than $10 to spend. How many braids can she get?

Guided Practice 1 Jessica wants to order some dvds from Amazon. Each dvd costs $15.99 and shipping for the entire order is $9.99. Jessica can spend no more than $100.

Guided Practice 2 The bowling alley charges a flat rate of $50 for a birthday party plus $5.50 for each person. Destiny can’t spend more than $100.

Ticket Out the Door The sum of 3 consecutive numbers is 33. Write an equation to represent the situation. Laquacious received an 82 on her first test and a 76 on her second test. Write an equation that could be used to figure out the score will she need to make on her third test in order to have a test average of 80. Cedrick’s mom told him that he could spend no more than $50 at the mall. He purchased a t-shirt for $20 and would like to purchase some new snap backs. If a snap back costs $9, write an equation or an inequality for the number of snap backs that Cedrick can buy.