1.4 – EQUATIONS

AND INEQUALITIES

SCHEDULE:Warm-Up

Review 1.1-1.3 Quiz1.4 Notes

Partner PracticeBegin Homework

WARM-UP Evaluate the following expressions.

63x

33x

3k k

when x = 24

when x = 4

when k = 12

1)

2)

3)

PAIR AND SHARE Compare your answers with the people

around you. Be prepared to share your answers with the class.

WARM-UP Evaluate the following expressions.

63x

33x

3k k

when x = 24

when x = 4

when k = 12

1)

2)

3)

WARM-UP What is an expression?

Give an example.

RECAPPING 1.1-1.3 QUIZ Review your 1.1-1.3 Quiz Make sure there are no grading errors

on it If there is anything you got wrong, it is

worth asking aboutLearn from your mistakesConcepts will reappear throughout all of

Algebra 1(A/B)

1.4 – EQUATIONS

AND INEQUALITIES

OBJECTIVE #1:Check solutions and SOLVE

equations using mental math.

Expressions are similar to equations because…

Expressions are different from equations because…

JOURNAL TIME

Vocabulary Equation:

An equation is made when an equal sign is used between two expressions creating a right and left side of the equation.

2 + 4 6

2 + 4 = 6

Vocabulary Open Sentence:

An equation that has one or more variables in it.

EXAMPLES?

Room must be silent Indicate your answer by:

Putting ONE FINGER up if you see an EXPRESSION

Putting TWO FINGERS up if you see an EQUATION

VOCABULARY CHECK

3x + 1 = 14

= EXPRESSION= EQUATION

7y - 6

= EXPRESSION= EQUATION

5x – 1 = 3

= EXPRESSION= EQUATION

5x – 1 = 3 + x

= EXPRESSION= EQUATION

Solutions of Equations When you take an equation and

replace the variables with numbers, you can make the statement either TRUE or FALSE. If it becomes true, then the number is called a SOLUTION of the equation.

IS IT A SOLUTION? Equation: 3x + 1 = 7

Is the number 1 a solution to the equation?

Is the number 2 a solution to the equation?

Is the number 3 a solution to the equation?

TAKE A GUESS: In your notes, make a prediction as to how many solutions there are for this equation.

Check whether 2, 3, or 4 are solutions of the equation 4x – 2 = 10.

SOLVING AN EQUATION This means you found ALL THE

SOLUTIONS of an equation. There are many tools we will learn

throughout the semester to solve equations.

Some are very easy and you can solve them in your head!

Example x + 2 = 5

Ask yourself the question, “What number can be added to 2 to obtain 5?”

Match the Equation with the Question

Equation Mental Math Question

1. x + 2 = 6 A. 2 times what number gives 10?

2. x – 3 = 4 B. What number divided by 3 gives 1?

3. 2x = 10 C. What number minus 3 gives 4?

4. D. What number cubed gives 8?

5. E. What number plus 2 gives 6?

13x

3 8x

1.4 – EQUATIONS

AND INEQUALITIES

OBJECTIVE #2:Check solutions of

inequalities in REAL-LIFE PROBLEMS.

INEQUALITY Another type of open sentence is called

an inequality. Inequalities have special symbols.Symbol Meaning

< is less than

> is greater than

< is less than or equal to

> is greater than or equal to

Matching

Inequality Sentence

1. x = 125A. no more than 125

2. x < 125 B. at least 125

3. x > 125 C. exactly 125

4. x < 125 D. less than 125

Room must be silent Indicate your answer by:

Putting ONE FINGER up if you see an EXPRESSION

Putting TWO FINGERS up if you see an EQUATION

Putting THREE FINGERS up if you see an INEQUALITY

VOCABULARY CHECK

5x < 8= EXPRESSION= EQUATION

= INEQUALITY

-7y2 + 8y= EXPRESSION= EQUATION

= INEQUALITY

3(x + 7) = 8= EXPRESSION= EQUATION

= INEQUALITY

SOLUTION OF AN INEQUALITY Number that makes a true statement

when it is substituted for a variable in an inequality.

Is 4 a solution of the inequality?

Step 1: Write inequalityStep 2: Substitute for variableStep 3: EvaluateStep 4: Conclusion (true or

false?)

2x – 1 < 8

Is 4 the ONLY solution of the inequality?

REAL-WORLD EXAMPLE The vet told Mr. V to restrict his dog’s

caloric intake to no more than 500 calories each day. Three times a day, Mr. V gives Nike a serving of food containing x calories. Set up an inequality to describe this situation.

Do the following values of x meet the vet’s restriction?170 calories165 calories

1.4 PAIRS PRACTICE Pair up with the person next to you Volume must stay down EACH STUDENT must show work on

a SEPARATE SHEET OF PAPER Work on odd problems only Stay focused

HOMEWORK 1.4 Practice Worksheet

Even problems onlyDue tomorrow!

Chapter 1 Test on Tuesday!