Writing Equations and Inequalities

Chapter 7 Lesson 1

Writing Equations in One Variable

Example 1

Writing Equations

​

Multiple Choice

Change the word sentence as an equation:

9 less than a number b equals 2.

• b-9=2

• b+9=2

• b-2=9

• bx2=9

Open Ended

Write the word sentence as an equation:

The product of a number g and 50 is 30.

Multiple Choice

A number k increased by 10 is the same as 24.

• 10+24=k

• k-10=24

• k+10=24

• k=24

​Two Step Inequalities

​Solving Two Step Inequalities

• The variable must be alone or isolated on one side of the inequality.

• Isolate the variable by using inverse or opposite operations. ​

• Whatever you do to one side ​you must do to the other.

​Two Step Inequalities

​Solving Two Step Inequalities

• When you multiply or divide BY a negative number, the inequality sign is flipped.

Multiple Choice

True or False:

10 + 3k < 22

Answers in the solution set will be negative

• True

• False

• Solution has the < or the > sign. ​

• The number in the solution will be included in the solution set. ​

​Closed Circle

• Solution has the < or the > sign

• The number in the solution will ​not be included in the solution set.

​Open Circle

​Graphing Two Step Inequalities

Multiple Choice

Which graph matches the inequality $$-5x\ge-15$$  ?

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Multiple Choice

Match the graph with its inequality.

• 11 < a
• 11 > a
•  11 ≤ a
•  11 ≥ a

Multiple Choice

When graphing b< 6 would you use an open or closed circle?

• Open
• closed

Multiple Choice

What is our first Golden Rule for Inequalities?

• Isolate the Variable

• Shade Appropriately

• Check the Order

• Circle the Constant on a Graph

Multiple Choice

22 < 6c + 4

• 11 > c

• 3 > c

• 11 < c

• 3 < c

Multiple Choice

Solve and graph the inequality.
77 ≤ 5 + 8n

• A
• B
• C
• D

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Multiple Choice

Choose the correct graph that best describes the solution for each inequality x + 5 ≥ 29

• a
• b
• c
• d

Multiple Choice

Solve the inequality $$18<\frac{x}{4}-2$$  

• $$80<x$$  

• $$5<x$$  

• $$4<x$$  

• $$64<x$$  

Multiple Choice

Which 3 values would make $$-3<\frac{3}{4}x$$   true?

• -2, 0, 12

• -4, -7, -16

• 0, -7, 13

• 23, -4, -10

Multiple Choice

Solve for k. 

7k – 2 ≥ -9

• k ≤ -1
• k≤1
• k≥1
• k ≥ -1

Poll

How do you feel about two step inequalities?

• I feel confident!

• I feel good!

• I feel okay, but I could use more practice.

• I have no idea what I'm doing!!!!!

writing equations from word problems

​

Multiple Select

words that represent "m" in

 $y=mx+b$  

• each

• fee

• every

• per

• total

Multiple Select

words that represent "b" in

 $y=mx+b$  

• each

• fee

• happens once

• total

• starts with

what is the important information we need to write an equation?

important info:

-$7 for EACH hour

-flat fee of $20

Fill in the Blank

write the equation in the form of

 $y=mx+b$   (no spaces)

Multiple Choice

 $y=7x+20$  

what does "x" represent?

• total cost 
  

• carts

• hours

• students

Multiple Choice

 $y=7x+20$  

what does "y" represent?

• total cost 
  

• carts

• hours

• students

Fill in the Blank

using your equation

 $y=7x+20$  
if the total cost was $76, what is the number of hours

what is the important information we need to write an equation?

important info:

-flat FEE of $275

-$20 PER person

-she can spend $1250 TOTAL

Multiple Choice

using the equation $y=mx+b\$  

what is m ?

• 275

• 20

• 1250

Multiple Choice

using the equation $y=mx+b\$  

what is b ?

• 275

• 20

• 1250

Multiple Choice

the $1,250 total she can spend represents 

• x

• y

Multiple Choice

what does x represent?

• total cost 

• price of food

• number of people

Fill in the Blank

write an equation to find the maximum number of guests she can invite (no spaces)

 $y=mx+b$  

Fill in the Blank

how many guests can she invite? (hint: your final answer should NOT be a decimal)

 $1250=20x+275$  

Multiple Choice

If chocolate chip cookies cost $3.00 per cookie plus $2 for boxing them up in a decorated box, what would the equation be?

• y=2x+3

• y=3x + 2

• y=3x + 2x

• y=5x

Multiple Choice

what does "x" represent?

• total cost

• number of cookies

• number of boxes

Multiple Choice

what does "y" represent?

• total cost

• number of cookies

• number of boxes

Multiple Choice

what would the total cost be for 14 cookies?

 $y=3x+2$  

• $4

• $24

• $42

• $44

Multiple Choice

On the first day of school, Miss Greenberg gave out 12 pencils. If she gives out 5 pencils each day to her students, which equation represents the total number of pencils she has given out?

• y=17x

• y=12x+5

• y=5x+12

• y=5x

Multiple Choice

On the first day of school, Miss Greenberg gave out 12 pencils. If she gives out 5 pencils each day to her students

what does x represent?

• pencils

• students

• days

• school

Multiple Choice

On the first day of school, Miss Greenberg gave out 12 pencils. If she gives out 5 pencils each day to her students.

what does y represent?

• pencils

• students

• days

• school

Multiple Choice

On the first day of school, Miss Greenberg gave out 12 pencils. If she gives out 5 pencils each day to her students, which equation represents the total number of pencils she has given out?

how many days have passed if she gives out 57 total pencils?

• 8

• 9

• 297

• 112

Writing Equations from Word Problems

​

Multiple Choice

If four times a number is increased by 15, then the result is three less than six times the number. Which equation can be used to find the value of the number?

• 4x + 15 = 6(x − 3)

• 4(x + 15) = 6x − 3

• 4x + 15 = 6x − 3

• 4x + 15 = 3 − 6x

Multiple Choice

If five times a number is subtracted from 27, the result is nine more than four times the number. Which equation can be used to find the value of the number?

• 5(27 - x) = 9 + 4x

• 27 - 5x = 4(9 + x)

• 27 - 5x = 4x + 9

• 5x - 27 = 9 + 4x

Multiple Choice

A number m increased by 23 is equal to 15 more than twice the number m.

• m + 23 = m + 15

• m + 23 = m² + 15

• m + 23 = 2m + 15

• m + 23 = 2(m + 15)

Multiple Choice

The equation below represents a situation.

40x = 1,000 + 0.30x Which word problem could the equation represent?

• Calculators cost $40 each at Tech Central. How many calculators can Mrs. Robinson buy for her class with $1,000 if the tax on each calculator is 30¢?

• Ivan deposits $1,000 in an account that earns interest at a rate of 30¢ per $1,000 per year. If he withdraws $40 every year, after how many years will his account be empty?

• Hyun owes Pablo $1,000, and his debt increases by 30¢ each day. If he saves $40 per day, after how many days will he be able to pay off his debt?

• Ada plans to give to charity $300 of every $1,000 she raises at a fundraiser. If she raises only $40, how much will she give to charity?

Multiple Choice

The equation below represents a situation.

2 + 4x = 4.5x Which word problem could the equation represent?

• Fernando can swim 4 meters per minute, and Jose can swim 4.5 meters per minute. If they start swimming northward from the same location at the sametime, after how many minutes will Jose be 2 meters ahead of Fernando?

• A certain number of square tiles with sides of length 4.5 inches are used to cover Ronnie's bedroom wall. If the same number of square tiles with sides of length 4 inches are used instead, 2 square inches would be left uncovered. How many tiles with sides of length 4.5 inches cover Ronnie's wall?

• Marco spends the same amount on movies every week. When the rental per movie is reduced from $4.50 to $4, he can rent 2 extra movies with his usual amount of money. How many movies per week does Marco usually rent?

• When the people at a party share several boxes of pizza evenly, each gets 4.5 pieces. If there had been 2 boxes fewer, each person would have gotten just 4 pieces. How many people are at the party?

Multiple Choice

The equation below represents a situation.

x − 1.5 = 6 − x Which word problem could the equation represent?

• Sasha bought 6 yards of material. She wants to cut it into 2 pieces so that the difference between the lengths of the pieces will be 1.5 yards. What would be the length, in yards, of one of the pieces?

• A container with 6 liters of water starts leaking into a bucket that already has 1.5 liters of water. How many liters of water will have leaked when the containers have the same amount of water?

• Sue had 2 identical pieces of material. She cut off 1.5 feet from one and attached it to the other to create a 6-foot curtain. What was the length, in feet, of each piece of material?

• Which number on a number line has the property that the distance between the number and 1.5 is the same as the distance between the number's opposite and 6?