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

1. Six time the difference of 5 times a number and 10.

2. 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 <

Fewer than Below Less than Smaller than

Less than or equal to ≤

No more than Not above Does not exceed At most Maximum

Greater than >

More than Exceeding Above Bigger than

Greater than or equal to ≥

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

1.

2.

3.

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.