What this lesson covers
- Why testing a point is two separate acts, computing and then comparing
- The boundary: what a strict sign refuses, and what ≤ and ≥ let in
- Reading the ordered pair in the right order, x first
- Systems: every inequality has to hold, and one failure ends it
- The same boundary arithmetic scored two opposite ways
Questions worked in the video
- 0:17Which ordered pair (x, y) is a solution to 3x - 2y < 12?
- 1:23Is (3, 5) a solution to the system y ≥ 2x - 1 and y < x + 4?
- 1:59Which ordered pair (x, y) is a solution to 5x + 4y ≥ 20?
Chapters
- 0:00Exactly 12 is not less than 12
- 0:17The setup
- 0:35Compute, then compare
- 1:23When both have to hold
- 1:59Your turn
- 2:38Three ways this goes wrong
- 3:00The bar decides
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The setup
The rule is three x minus two y is less than twelve. Four ordered pairs, exactly one of them works. This is the most common inequality question on the digital SAT, and it needs no graph at all.
0:35Compute, then compare
Substitute both coordinates, then compute. Choice A is six and three. Three times six is eighteen. Two times three is six. Eighteen minus six is twelve. Hold that number. Now compare it to the rule. Is twelve less than twelve? No. Twelve is equal to twelve. That point sits exactly on the boundary line, and a strict less than never lets the boundary in. Choice A is out. Run the rest. Eight and four gives sixteen, too big. Seven and one gives nineteen, too big. Two and five gives six minus ten, which is negative four. Negative four really is less than twelve. Answer C.
1:23When both have to hold
Now a system. y is greater than or equal to two x minus one, and y is less than x plus four. A point has to satisfy every inequality, not just the first one. Test three and five. Two times three minus one is five. Five is greater than or equal to five. True, and true only because that sign carries the bar. Then three plus four is seven, and five is less than seven. Both hold, so it is a solution. Move to three and eight and the second one fails. Stop right there.
1:59Your turn
Your turn. Which ordered pair satisfies five x plus four y is greater than or equal to twenty? Ten seconds. One and three gives seventeen, short. Zero and four gives sixteen, short. Two and two gives eighteen, short. Four and zero gives exactly twenty. And this time the sign carries the bar, so exactly twenty is allowed in. Answer D.
2:38Three ways this goes wrong
Three ways this goes wrong. One, letting the boundary in under a strict sign, when twelve is not less than twelve. Two, dropping the minus and adding two y instead of subtracting it, which rejects the right answer. Three, checking one inequality in a system and stopping there.
3:00The bar decides
Substitute, compute, then compare. The bar decides the boundary.
Read the written version: the Linear inequalities strategy guide, then try 25 hard Linear inequalities questions with full explanations. Both are free, no account needed.