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Mathematics 67 Online
mikewwe13:

Which of the following inequalities have -8 in its solution set? A. 0 < x+4 < 1 B. Three less than a number is at least -5 and at most 2. C. The sum of 8 times a number and 7 is between -1 and 1. D. 3x ≥ 24 or 3x ≤ -24

mikewwe13:

@Vocaloid

Vocaloid:

notice how some of them are written as words and some are written as mathematical variables/numbers. to make it easier, express them all as math for example: Three less than a number is at least -5 and at most 2. "three less than a number" is x - 3 at least -5 and at most 2 translates to -5 <= x -3 <= 2 repeat this process with "The sum of 8 times a number and 7 is between -1 and 1."

mikewwe13:

the answer is D am i correct ?

Vocaloid:

yeah that's right

mikewwe13:

i calculated it

mikewwe13:

that's right ?

mikewwe13:

The following graph represents an inequality. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei3_1_201.png Which inequality is represented by this graph? A. -3 ≤ x ≤ 3 B. -3 ≤ x < 3 C. -3 < x ≤ 3 D. -3 < x < 3

Vocaloid:

notice how both of the red dots at the end are closed circles (they're filled in red instead of being empty) that means both the -3 and the 3 need ≤ symbols which answer choice matches this description?

mikewwe13:

C

mikewwe13:

am i correct ?

Vocaloid:

nope which answer choice has two ≤ symbols?

mikewwe13:

A

Vocaloid:

good, A

mikewwe13:

Which of the following inequalities have -6 in its solution set? A. 5x > 35 or 5x < −35 B. Two less than a number tripled is at least -5 and at most 1. C. The sum of 3 times a number and 5 is between -16 and 11. D. -8 < x−5 < 3

Vocaloid:

again, translate the words to variables/math and see which one is true for x = -6

mikewwe13:

it's either B or C

mikewwe13:

the answer is B

Vocaloid:

"The sum of 3 times a number and 5 is between -16 and 11." how would you express this as a mathematical expression?

mikewwe13:

3x + 5 < -16 + 11

Vocaloid:

almost "between -16 and 11" means -16 < ___ <11 so -16 < 3x + 5 < 11 does x = -6 make this inequality true?

mikewwe13:

yes

Vocaloid:

good, so C is your answer

mikewwe13:

The following graph represents an inequality. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei3_1_203.png Which inequality is represented by this graph? A. -6 ≤ x ≤ 3 B. x ≤ 6 or x > 3 C. x < −6 or x ≥ 3 D. -6 < x ≤ 3

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