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One-Variable Equations and Inequalities Videos 30 videos
You don't want to leave a bunch of unsolved rational equations sitting around.
Solving inequalities using blob fish? Yes, please!
ACT Math: Coordinate Geometry Drill 1, Problem 1. Which inequality is expressed by the number line?
ACT Math 1.3 Coordinate Geometry 304 Views
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Description:
ACT Math: Coordinate Geometry Drill 1, Problem 3. Solve the inequalities and choose the correct graph.
- Coordinate Geometry / Real number lines and inequalities
- Product Type / ACT Math
- Foreign Language / Arabic Subtitled
- Foreign Language / Spanish Subtitled
- Foreign Language / Korean Subtitled
- Foreign Language / Chinese Subtitled
- Coordinate Geometry / The relations between equations and graphs
- Coordinate Geometry / Graphing inequalities
Transcript
- 00:02
For a good time, solve this shmoopy question.
- 00:05
Solve the inequalities and choose the correct graph: -4 ≤ 2y + 2 < 8.
- 00:11
And here are your potential options...
- 00:15
For starters, let's break this into 2 problems.
- 00:18
We'll start by lopping off 8 at the end there and just consider:
Full Transcript
- 00:22
Negative 4 is less than or equal to 2y plus 2.
- 00:27
We subtract 2 from both sides to get:
- 00:29
Negative 6 is less than or equal to 2y.
- 00:32
Then we divide both sides by 2 to get:
- 00:35
Negative 3 is less than or equal to y.
- 00:38
So...let's put this part on the graph...
- 00:40
We start here at negative 3 ... and y is greater than or equal to this number so we're going
- 00:44
to move to the right...
- 00:46
And suddenly, we can eliminate B and D. Note that D has an open circle over negative 3...
- 00:50
...meaning that it's NOT equal to it but only greater than 3.
- 00:54
For our equation, it's greater than or equal... so the answer has to be A, C or E.
- 01:00
OK now consider the second part of the equation separately:
- 01:03
2y plus 2 is less than 8...
- 01:05
Subtract 2 from both sides and we have:
- 01:07
2y is less than 6.
- 01:09
Divide both sides by 2 and y is less than 3.
- 01:12
So let's put this part on the graph - and note that we need the open circle above
- 01:17
positive 3 here because it's not equal to it...
- 01:20
So the area we're talking about is between here and here.
- 01:23
Only A works and that's pretty much it.
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You don't want to leave a bunch of unsolved rational equations sitting around.
Solving inequalities using blob fish? Yes, please!