Creating Equations and Inequalities from Word

ProblemsUnit 1, Day 4

Compare and contrast your slip of paper with other class mates.

Your slips of paper can be separated into three distinct groups.

Find all other classmates that you believe should go into your group.

Once everyone in the class belongs to a group, decide as a group if you agree that everyone’s slip belongs in that group.

Once you agree, decide on a label that best describes all slips of paper in your group. (Keep it quite!)

Warm-up

How do I translate “8x=24” into a written statement? Eight times a number is 24 This is an equation How do I translate “fourteen times a number added

to three” into a numerical statement? 14p + 3 This is an expression How do I translate “2/y > 4w” into a written

statement? Two divided by a number is greater than four times

another number This is an inequality

Review: Translating basic problems

Word problems offer you a context. Word problems often give you more

information than necessary Word problems can usually be simplified

into basic problems (something you already know how to work with!)

Translating Word Problems

Look for your goal Read through the entire problem and get a

goal in mind Your goal should be what the problem is

asking you to do

Steps to Translating:

Define your variables Look for something we are trying to find

(goal) or do not know Decide what you are going to call your

variables

Steps to Translating:

Cross out unimportant information Ignore or cross out any added filler in

problems Specifically, look for numbers that will not

help you in reaching your goal

Highlight important information Look for numbers already given Look for math phrases

Steps to Translating:

Write out your equation or inequality Use all the information you decided was

important and all of your variables

Steps to Translating:

Check that your answer matches your goal Go through the word problem one more

time, phrase by phrase, and make sure everything in it matches up to how you would read your numerical problem.

Then, make sure you have answered what the problem actually asked.

Steps to Translating:

Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement.

Example #1

Model an equation of Suzanne’s old balance to her new balance

Goal

Variables

Solving: Follow through your steps

d=number of dollars Suzanne withdrew

Highlight important information

Solving: Follow through your steps

Cross out unimportant information Suzanne made a withdrawal of d dollars

from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement.

Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement.

350 – d = 280

Write your equation or inequality

Check that your answer matches your goal

Solving: Follow through your steps

Eleni is x years old. In thirteen years she will be twenty-four years old. Model her age as a mathematical statement.

Example #2

A large pizza pie with 15 slices is shared among p students so that each student's share is 3 slices. Model each student’s share.

Example #3

Using Inverse Operations to Solve Equations and

InequalitiesUnit 1, Day 5

Inverse: the direct opposite The inverse operation “cancels out” an

original operation in the equation or inequality

Mathematical operations performed on one side of the equation/inequality must be performed on the other side to keep the statement true

Inverse Operations

The inverse operation of Addition is…

The inverse operation of Subtraction is…

The inverse operation of Multiplication is…

The inverse operation of Division is…

The inverse operation of squaring is…

The inverse operation of taking the square root is…

Inverse Operations

SubtractionAddition

Taking a square root

Multiplication

Division

Squaring

Inverse Operation Examples

35𝑥=6 𝑥=6÷

35 𝑥=

6153 𝑥=10

𝑥=5𝑥2=25 √𝑥2=√25

𝑥+5−5=25−5𝑥+5=25 𝑥=20

Solving Algebraic Equations in One VariableTo solve equations we must follow these rules:

(1) Take care of any Distributive Property or any other Multiplication/Division found in the equation.

(2) Combine Like Terms on the left and right of the equal sign individually.(3) Move the variables to one side of the equation and the constants to the other side (isolate the variable) using inverse operations.(4) Get the variable alone (coefficient of 1) by dividing each side of the equation by the variable’s coefficient.

You may have to use the reciprocal of the coefficient if there is a fraction attached to the variable in the last step.

Practice Problems - Equations

1.

2.

3.

4.

CHECK YOUR SOLUTIONS!

x = 3

w

b = -63

y = 4

1.

2.

3.

4.

5.

Practice Problems - Inequalities

CHECK YOUR SOLUTIONS!

𝑦 ≥3

3

𝑥>9

Follow the same rules as solving equations EXCEPT

When multiplying or dividing by a negative, be sure to flip your inequality sign.

Solving Algebraic Inequalities

A number is divided by 3. Then 14 is added to the quotient. The result is 33.What is the original number?

Landon has 37 baseball cards. If 4 cards can fit on one page, how many pages does Landon need to buy?

Creating and Solving Equations

The square root of a number is subtracted from the sum of the number and 12. The result is 42. What is the original number?

Kata has a savings account that contains $230. She decides to deposit $5 each month from her monthly earnings for baby-sitting after school. Write an expression to find how much money Kata will have in her savings account after X months. Let X represent the number of months. Then find out how much she will have in her account after 1 year.

You Try!