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BvU

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Both lines apply to the product, that changes sign both at x = -1 and at x = 7. From the +++ and the - - - you can conclude the sign of the product.

- #3

HallsofIvy

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The second row shows where x- 1 is negative and positive- it is negative for all x< 1, positive for all x> 1.

Since the product of two negative or of two positive number is positive while the product of one negative and one positive number is negative, the diagram shows that the product (x- 7)(x- 1) is positive for x< 1, where both factors, (x- 7) and (x- 1), are negative, positive for x> 7where both factors, (x- 7) and (x- 1), are positive, and negative for 1< x< 7 where (x- 7) is negative and (x- 1) is positive.

- #4

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got it Thank you !

The second row shows where x- 1 is negative and positive- it is negative for all x< 1, positive for all x> 1.

Since the product of two negative or of two positive number is positive while the product of one negative and one positive number is negative, the diagram shows that the product (x- 7)(x- 1) is positive for x< 1, where both factors, (x- 7) and (x- 1), are negative, positive for x> 7where both factors, (x- 7) and (x- 1), are positive, and negative for 1< x< 7 where (x- 7) is negative and (x- 1) is positive.

- #5

mathman

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The formula in the diagram is (x-7)(x+1).the representation of the inequality (x-7)(x-1) ≤ 0 makes no sense to me . can someone explain this .

the diagram is attached

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- #6

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correct ,sorry

- #7

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There's nothing true in cross multiplication we divide both sides by zero and it gives 0/0 is 0/0. Sorry I got away from topic but I thought it would help and makes maths interesting and fun.

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