What this lesson covers
This one solves a two-sided inequality down to a range, shows three entries that all score, and then the two that do not: the endpoint, which a strict inequality leaves out, and both answers typed together.
00:00 Two answers, both right
00:14 Read the stem
00:34 The method
01:08 Three ways this goes wrong
01:23 Recap
The inequality question is original, written for SAT Climb. The "enter only one answer" rule is quoted from the official Bluebook test directions.
Worked examples
The questions the video works, written out: the setup, each step, the answer and the trap.
0:34Example 1
and . What is one possible value of x?
- Read the stem first. One possible value means more than one number works, and the rule for that case is short: enter one of them. The value of x or the positive solution would mean exactly one.
- Write the two inequalities as one: . Take 2 off all three parts: .
- Divide everything by 3: .
- Anything strictly between 3 and 6 works: 4, 5, 4.5 and so on. Pick one and type only that. 4 is one character; 4.5 is three and fits too.
- Check with 4: 3(4) + 2 = 14, and 14 is greater than 11 and less than 20.
Answer: Any single value with 3 < x < 6, for example 4
The box takes one number, and any number inside the open interval scores. Three near misses score zero. 4, 5 is two answers when the box asked for one. 3 lands on the endpoint, and a strict inequality leaves the ends out: 3(3) + 2 = 11, which is not greater than 11. 3<x<6 types the whole statement into a box that only takes a number.
One more, same method
What is one possible value of x?
- The stem says one possible value, so expect more than one solution and plan to enter one of them.
- A product is zero when one of its factors is zero. x + 3 = 0 gives x = -3. x - 5 = 0 gives x = 5.
- Check both: (-3 + 3)(-3 - 5) = 0(-8) = 0, and (5 + 3)(5 - 5) = 8(0) = 0.
- Type -3, which uses two of the six cells a negative answer gets, or type 5. Not both.
Answer: -3 or 5, entered as a single value
Either root scores on its own. The trap is showing the whole answer: -3, 5 and -3 or 5 both hand the box two values and score zero. Had the stem asked for the positive solution, only 5 would count, which is why the stem gets read before the algebra starts.
Lesson transcript
The narration of the video, word for word, under its chapter headings.
Some grid-ins have more than one right answer, and the stem tells you which kind you are looking at. One possible value means many work. The value, or the positive solution, means exactly one. If more than one works, the rule is short: enter one of them. Three x plus two is greater than eleven, and less than twenty. Take two off all three parts. Three x sits between nine and eighteen. Divide everything by three. x is between three and six. So four works. Five works. Four point five works. Type any one of them and you score. Three does not, because the inequality was strict. And typing four comma five hands the box two answers when it asked for one. Three ways this goes wrong. Typing two values. Landing on the endpoint, which a strict inequality leaves out. And typing the whole inequality, when the box only takes a number. Many right answers. Type one.