Solve One-Step Inequalities Using Addition and Subtraction
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by Felix Gabathuler
| 41 Questions
Objective of the Day: Today I (which is you), will be able to solve one step inequalities using addition or subtraction AND graph the result on a number line. I'll also be able to model real life situations using inequalities and solve them too! Wooo big big big day!!
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First, let's start out testing solutions to inequalities. For example, if x > 3, would -5 be a solution?
Yes
IDK (Never a good answer...)
No
If you need a refresher on how to test a solution or what that means, watch the video below. If you're confident in your skills, move on to the following practice.
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Now, click on the blue text below to test your knowledge. Remember, raise your hand and ask Mr. Felix for help if needed! Or turn to your partner and ask them for help!

Also, make sure you are logged into Khan Academy so Mr. Felix can see all those 100%s you get!

Testing Solutions to Inequalities

When you're done, click on the most fitting answer below.
I answered 100% correct... or maybe just got ONE wrong... BUT I know what I'm doing and could get 100% if I tried again!
I.... well I... didn't do it...
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Now that you've finished testing solutions, describe how you could use this knowledge to help graph an inequality on the number line. How does testing solutions help you "Petr Cech" your answers...? Does it help you figure out which way your solution arrow is pointing?
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Now let's start translating these inequalities to graphs on a number line. Quick question, if you see an inequality on a number line, what does the bold arrow pointing in one direction mean?
It represents the numbers that could NOT be solutions to the inequality
What arrow? Is this PE class?
It represents which way the wind is blowing
It represents the numbers that could be solutions to the inequality
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Another quick question, how do I represent a less than or equal to symbol on the number line?
With an open square
With an open circle
With a closed square
With a closed circle
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Last quick question, in the inequality y ≤ -3.4 , what is the critical value?
-3.4
y
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Ok really, this is the last quick question: in the inequality z > 14 , what is are the possible solutions of z? Choose all that apply.
|-15|
-13.9
58/3
13.9
-2
12
Now, watch the following videos if you need a refresher on how to graph an inequality or if you want to see an example of an inequality graphed on a number line. If you're good, move on to the following excercise.
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Now, click on the blue text below to test your knowledge. Remember, raise your hand and ask Mr. Felix for help if needed! Or turn to your partner and ask them for help!

Also, make sure you are logged into Khan Academy so Mr. Felix can see all those 100%s you get!

Plotting Inequalities

When you're done, click on the most fitting answer below.
I answered 100% correct... or maybe just got ONE wrong... BUT I know what I'm doing and could get 100% if I tried again!
I.... well I... didn't do it...
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Now, enough of picking some multiple choice answers. I want to see you draw your own graph. Click on the box below and graph the given inequality. Consider this a graphing inequalities formative. Play around with the tool bar on your left to make circles, draw lines, and use different colors. Take it seriously and try it without notes! Good luck!!
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Try one more. I bet you're getting reaaaaaaaaaal good at it!
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Let's put this all together and write our own inequalities. Click on the following link to complete the challenge!!

Writing Inequalities Challenge
Challenge accepted and completed!! I only missed a maximum of one question!
Not done yet, but I'm trying!
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The quote above was obviously talking about One-Step Inequalities. In your opinion, why are these inequalities called one step? What does that one step mean? Be specific please!
If you are confident in your solving One Step inequalities abilities using addition or subtraction, skip the next video. If you'd like to see an example worked out, then give it a click.
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Solve the inequality: x + 7 ≥ 18
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Solve the inequality: -12 < y - 6
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Solve the inequality:

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Solve the inequality in the box below and graph the solution. Use the text box to write the solution. Hint: on a Mac, use "option" and > or < to write ≤ or ≥
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Solve the inequality in the box below and graph the solution. Use the text box to write the solution. Hint: on a Mac, use "option" and > or < to write ≤ or ≥
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Solve the inequality in the box below and graph the solution. Use the text box to write the solution. Hint: on a Mac, use "option" and > or < to write ≤ or ≥
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Which number line represents 13 > x +11 ?

zoom_in

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A person can be no taller than 6.25 feet to become an astronaut pilot for NASA. Your friend is 5 feet 9 inches tall. Write and solve an inequality that represents how much your friend can grow(g) and still meet the requirement. Note, 12 inches equals 1 foot.
5.75 + 𝑔 ≤ 6.25
5.75 + 𝑔 ≥ 6.25
5.75 + 𝑔 > 6.25
5.75 + 𝑔 < 6.25
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Describe and correct the error in solving the inequality or graphing the solution of the inequality.
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Solve an inequality that represents x. The perimeter is less than 27 feet.
zoom_in

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The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground. Draw a diagram to model the situation. Then write and solve an inequality that represents the required length of the post.
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The possible values of x are given by x + 8 ≤ 6. What is the greatest possible value of 7x?
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Answer ALL THREE of the questions in the box below.
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If you've gotten this far, bravo to you!!

So, we've been working on solving inequalities using addition and subtraction. You figured out that it's really similar, no... exactly like, solving equations. Now we're going to take it one step further. Let's start solving inequalities using multiplication or division.

Do you think it's going to be the same or different?
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Solve this inequality for x: 2x < 4
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What are some solutions to the above inequality? Click all that apply.
1
0
-5
10
2
-1
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Solve this inequality for x:

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What are some solutions to the above inequality? Click all that apply.
1
0
-5
10
2
-1
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Here's where things get interesting....

Solve this inequality for x: -3x < 9


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What are some solutions to the above inequality? Click all that apply.
6
3
-5
4
0
-1
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What did you notice about the solutions? Did anything take you by surprise? Can you make a generalization about solving an inequality when you have to multiply or divide by a negative number?
Watch the videos below for extra help! If you think you're ready for some practice, skip them and move on to the following excercises.
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Click on the blue link to practice all kinds of one step inequality problems:

Solving One Step Inequalities - Multiplication and Division
Done and I've got it!!!
Don't get it... need help!
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Now try solving and graphing a few on your own! You should have two answers: the solution and the graph. Test some solutions to "Cech" your answers!
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Now try solving and graphing a few on your own! You should have two answers: the solution and the graph. Test some solutions to "Cech" your answers!
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Now try solving and graphing a few on your own! You should have two answers: the solution and the graph. Test some solutions to "Cech" your answers!
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