ALGEBRA 1

Lesson 3-1 Warm-Up

ALGEBRA 1

Lesson 3-1 Warm-Up

ALGEBRA 1

“Inequalities and Their Graphs” (3-1)

What is an “inequality”?

What is the “solution of an inequality”?

How do you find all of the “solution of an inequality”?

inequality (“in” means “not” and “equality” means “equal”): a number sentence that uses the inequality symbols <, >, ≤, or ≥ to show that the left side of the inequality symbol is may be “less than”, “greater than”, “less than or equal to”, or “greater than or equal” to the right side.

solution of an inequality: any number that makes the inequality true (Usually, there will be an infinite number of solutions to an inequality.)

Example: The “solutions of the inequality” x < 3 are all of the numbers that are less than 3.

Tip: To find all of the solutions of an inequality, solve for the variable the same way you would if you were working with an “=“ sign by undoing operations until you have a variable on one side of the inequality sign and a number on the other. Then, graph the solutions on a number line.

ALGEBRA 1

“Inequalities and Their Graphs” (3-1)

How do you turn a written inequality into a graph?

How do you turn a graph into a written inequality?

You can also write -1 ≥ a as a ≤ -1.

ALGEBRA 1

Is each number a solution of x 5?>

Yes, 5 5 is true. >

No, –2 5 is not true. >

Yes, 10 5 is true.>

a. –2

b. 10

c. 25 5

Inequalities and Their GraphsLESSON 3-1

Additional Examples

ALGEBRA 1

Is each number a solution of 3 + 2x < 8?

a. –2 b. 3

3 + 2x < 8

–2 is a solution.

3 + 2x < 8

3 is not a solution.

3 + 2(3) < 8

3 + 6 < 8

9 < 8

3 + 2(–2) < 8 Substitute for x.

3 – 4 < 8 Simplify.

–1 < 8 Compare.

Inequalities and Their GraphsLESSON 3-1

Additional Examples

ALGEBRA 1

b. Graph –3 ≥ g.

The solutions of d < 3 are all the points to the left of 3.

The solutions of –3 ≥ g are –3 and all the points to the left of –3.

a. Graph d < 3.

Inequalities and Their GraphsLESSON 3-1

Additional Examples

ALGEBRA 1

Write an inequality for each graph.

x < 2 Numbers less than 2 are graphed.

x > –2 Numbers greater than –2 are graphed.

x –3 Numbers less than or equal to –3 are graphed.<

a.

b.

c.

d. x > Numbers greater than are graphed.12

12

Inequalities and Their GraphsLESSON 3-1

Additional Examples

ALGEBRA 1

Define a variable and write an inequality for each situation.

a. A speed that violates the law when the speed limit is 55 miles per hour.

b. A job that pays at least $500 a month.

Let i = an illegal speed.

The speed limit is 55, so i > 55.

The job pays $500 or more, so p 500.>

Let p = pay per month.

Inequalities and Their GraphsLESSON 3-1

Additional Examples

ALGEBRA 1

1. Is each number a solution of x > –1?

a. 3 b. –5

2. Is 2 a solution of 3x – 4 < 2 ?

3. Graph x > 4.

4. Write an inequality for the graph.  

5. Graph each inequality.

a. t is at most 2. b. w is at least 1.

yes no

no

p –2<

Inequalities and Their GraphsLESSON 3-1

Lesson Quiz