confidential 1 algebra1 graphing and writing inequalities
TRANSCRIPT
![Page 1: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/1.jpg)
CONFIDENTIAL 1
Algebra1Algebra1
Graphing and Graphing and WritingWriting
InequalitiesInequalities
![Page 2: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/2.jpg)
CONFIDENTIAL 2
Warm UpWarm Up
1) 2b - 6 = b + 3
3) 2 (y + 1) = 2y + 1
4) x + (x + 1) + (x + 2)
5) 5 + (x + 3) + 5 + 2 (x + 3)
Solve each equation.
2) -3 (2 - x) = 5x + 2
Simplify each expression.
1) b = 9 2) b = 9
3) contradictory statement
4) 3x + 3
5) 3x + 19
![Page 3: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/3.jpg)
CONFIDENTIAL 3
Inequalities
An inequality is a statement that two quantities are not equal. The quantities are compared by using one
of the following signs:
A < B
A > B
A ≤ B
A ≥ B
A ≠ B
Where, A and B are some integer value.
![Page 4: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/4.jpg)
CONFIDENTIAL 4
Any number that makes an inequality true is a solution of the inequality.
For example: -4 is a solution of y ≥ -5because -4 ≥ -5.
Inequalities, like equations, can be true, false or open.
15 > 11
6 < 3
a < 20
This sentence is true.
This sentence is false .This sentence is open. It is neither true nor false until “a" replaced with a number.
![Page 5: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/5.jpg)
CONFIDENTIAL 5
< > ≤ ≥ ≠ Less than Fewer than
Greater than More than Exceeds
Less than or equal to No more than At most
Greater than or equal to No less than At least
A is not equal to B.
Many situations in real life can be described using inequalities. The table below shows some of the
common phrases and corresponding inequalities.
![Page 6: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/6.jpg)
CONFIDENTIAL 6
Describe the solutions of 3 + x < 9 in words.
Identifying Solutions of Inequalities
Test values of x that are positive, negative, and 0.
When the value of x is a number less than 6, the value of 3 + x is less than 9.
When the value of x is 6, the value of 3 + x is equal to 9.
When the value of x is a number greater than 6, the value of 3 + x is greater than 9.
x -2.75 0 5.99 6 6.01
3 + x -5.75 3 8.99 9 9.01
3 + x < 9 -2.75 < 9 3 < 9 8.99 < 9 9<9 9.01< 9
Solution? Yes Yes Yes No No
![Page 7: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/7.jpg)
CONFIDENTIAL 7
1. Describe the solutions of 2p > 8 in words.
Now you try!
1) p > 4. When the value of p is a number greater than 4, the value of 2p > 8 is greater than 8.
![Page 8: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/8.jpg)
CONFIDENTIAL 8
An inequality like 3 + x < 9 has too many solutions to list. You can use a graph on a number line to
show all the solutions.
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x < 6
The solutions are shaded and an arrow shows that the solutions continue past those shown on the graph. To show that an endpoint is a solution, draw a solid circle
at the number. To show that an endpoint is not a solution, draw an empty circle.
![Page 9: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/9.jpg)
CONFIDENTIAL 9
Graphing Inequalities
WORDS ALGEBRA
All real numbers less than 5 x < 5
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x < 5
All real numbers greater than -1 x > -1
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x > -1
![Page 10: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/10.jpg)
CONFIDENTIAL 10
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x ≥ 0
WORDSALGEBRA
All real numbers greater than or equal to 0 x ≥ 0
All real numbers less than or equal to 1 x ≤ 1 2 2
0 1 2 3 4 5 6-5 -4 -3 -2 -1
x ≥ 1 2
![Page 11: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/11.jpg)
CONFIDENTIAL 11
Graphing Inequalities
The solution of inequality x < 9 represented on the number line is
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x < 9
A) Solve: Graph the solution of he inequality, x < 9 on the number line.
An open dot shows that 9 is not a solution. Draw an arrow pointing to the left.
Shade all points to the left of 9.
![Page 12: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/12.jpg)
CONFIDENTIAL 12
The solution of inequality x ≥ -3 represented on the number line is
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x ≥ -3
B) Solve: Graph the solution of the inequality, x ≥ -3 on the number line.
An solid circle shows that -3 is a solution. Draw an arrow pointing to the right.
Shade all points to the right of -3.
![Page 13: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/13.jpg)
CONFIDENTIAL 13
Graph each inequality.
Now you try!
1) c > 2.5 2) 22 - 4 ≥ w
2.5
0 1 2 3 4 5 6-5 -4 -3 -2 -1
2.5
1)
2)2.5
0 1 2 3 4 5 6-5 -4 -3 -2 -1
0
![Page 14: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/14.jpg)
CONFIDENTIAL 14
Writing an Inequality from a Graph
Write the inequality shown by each graph.
2.5
0 1 2 3 4 5 6-5 -4 -3 -2 -1
Use any variable. The arrow points to the right, so use either > or ≥. The empty circle at 4.5 means that 4.5 is
not a solution, so use >.
x > 2.5
A)
2.5
x > 2.5
![Page 15: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/15.jpg)
CONFIDENTIAL 15
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
B)
Use any variable. The arrow points to the left, so use either < or ≤. The solid circle at -5 means that -5 is a
solution, so use ≤.
x ≤ -5
- 5
![Page 16: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/16.jpg)
CONFIDENTIAL 16
1. Write the inequality shown by the graph.
Now you try!
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
- 0.5
The open dot and the left arrow from point -0.5 shows the value x < -0.5
![Page 17: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/17.jpg)
CONFIDENTIAL 17
Solution:
A) The members of a lightweight crew team can weigh no more than 165 pounds each. Define a variable and write
an inequality for the acceptable weights of the team members. Graph the solutions.
Sports Application
Let w represent the weights that are allowed.
i.e., w ≤ 165
Stop the graph at 0 because a person’s weight must be a positive number.
105 120 135 150 1650 15 30 45 60 75 90
![Page 18: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/18.jpg)
CONFIDENTIAL 18
1. A store’s employees earn at least $8.25 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.
Now you try!
1) x ≥ 8.25
2 3 4 5 6 7 8 9 10-1 0 1
8.25
![Page 19: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/19.jpg)
CONFIDENTIAL 19
Assessment
Describe the solutions of each inequality in words.
1) g - 5 ≥ 6 2) -2 < h + 1
3) 20 > 5t
1) g ≥ 11. When the value of g is a number greater than 11, the value of g - 5 is greater than 9.
2) h > -3. When the value of h is a number greater than -3, the value of h + 1 is greater than -2.
3) t < 4. When the value of t is a number less than 4, the value of 5t is less than 20.
![Page 20: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/20.jpg)
CONFIDENTIAL 20
Graph each inequality.
4) x < -5 5) (4 - 2)3 > m
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
4)
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
5)
-5-5
8
![Page 21: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/21.jpg)
CONFIDENTIAL 21
Write the inequality shown by each graph.
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
6) x ≤ - 5
6)
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
7) x > 2.5
7)
![Page 22: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/22.jpg)
CONFIDENTIAL 22
Define a variable and write an inequality for each situation. Graph the solutions.
8) There must be at least 20 club members present in order to hold a meeting.
9) A trainer advises an athlete to keep his heart rate under 140 beats per minute.
10) The maximum speed allowed on Main Street is 25 miles per hour.
8) x ≥ 20
9) x < 140
10) x ≤ 25
![Page 23: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/23.jpg)
CONFIDENTIAL 23
Inequalities
An inequality is a statement that two quantities are not equal. The quantities are compared by using one
of the following signs:
A < B
A > B
A ≤ B
A ≥ B
A ≠ B
Where, A and B are some integer value.
Let’s review
![Page 24: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/24.jpg)
CONFIDENTIAL 24
< > ≤ ≥ ≠ Less than Fewer than
Greater than More than Exceeds
Less than or equal to No more than At most
Greater than or equal to No less than At least
A is not equal to B.
Many situations in real life can be described using inequalities. The table below shows some of the
common phrases and corresponding inequalities.
![Page 25: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/25.jpg)
CONFIDENTIAL 25
Describe the solutions of 3 + x < 9 in words.
Identifying Solutions of Inequalities
Test values of x that are positive, negative, and 0.
When the value of x is a number less than 6, the value of 3 + x is less than 9.
When the value of x is 6, the value of 3 + x is equal to 9.
When the value of x is a number greater than 6, the value of 3 + x is greater than 9.
x -2.75 0 5.99 6 6.01
3 + x -5.75 3 8.99 9 9.01
3 + x < 9 -2.75 < 9 3 < 9 8.99 < 9 9<9 9.01< 9
Solution? Yes Yes Yes No No
![Page 26: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/26.jpg)
CONFIDENTIAL 26
An inequality like 3 + x < 9 has too many solutions to list. You can use a graph on a number line to
show all the solutions.
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x < 6
The solutions are shaded and an arrow shows that the solutions continue past those shown on the graph. To show that an endpoint is a solution, draw a solid circle
at the number. To show that an endpoint is not a solution, draw an empty circle.
![Page 27: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/27.jpg)
CONFIDENTIAL 27
Graphing Inequalities
The solution of inequality x < 9 represented on the number line is
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x < 9
A) Solve: Graph the solution of he inequality, x < 9 on the number line.
An open dot shows that 9 is not a solution. Draw an arrow pointing to the left.
Shade all points to the left of 9.
![Page 28: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/28.jpg)
CONFIDENTIAL 28
The solution of inequality x ≥ -3 represented on the number line is
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
x ≥ -3
B) Solve: Graph the solution of the inequality, x ≥ -3 on the number line.
An solid circle shows that -3 is a solution. Draw an arrow pointing to the right.
Shade all points to the right of -3.
![Page 29: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/29.jpg)
CONFIDENTIAL 29
Writing an Inequality from a Graph
Write the inequality shown by each graph.
2.5
0 1 2 3 4 5 6-5 -4 -3 -2 -1
Use any variable. The arrow points to the right, so use either > or ≥. The empty circle at 4.5 means that 4.5 is
not a solution, so use >.
x > 2.5
A)
2.5
x > 2.5
![Page 30: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/30.jpg)
CONFIDENTIAL 30
0 1 2 3 4 5 6 7 8 9 10 11 12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
B)
Use any variable. The arrow points to the left, so use either < or ≤. The solid circle at -5 means that -5 is a
solution, so use ≤.
x ≤ -5
- 5
![Page 31: CONFIDENTIAL 1 Algebra1 Graphing and Writing Inequalities](https://reader036.vdocuments.mx/reader036/viewer/2022062322/5697bfae1a28abf838c9c66d/html5/thumbnails/31.jpg)
CONFIDENTIAL 31
You did a great job You did a great job today!today!