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3 years ago

URGENT!! Given the inequality, the test point (2,-8) .... a) b) c) d)

Mathematics

1 answer:

sattari [20]3 years ago

3 0

Answer:

Step-by-step explanation:

let's see, I'd the point on the line/boundary ?

for this we use the equality part (and use the coordinates of the point as x and y) :

-8 = 2×2² - 5×2 - 6 = 8 - 10 - 6 = -2 - 6 = -8

correct.

this proves that the point is on the line defined by the equation.

and that means it is on the boundary of the inequality.

because that inequality contains the boundary in the solution region (hence the >= relation instead of just >), we cannot use that point to determine which side of the boundary (incl. the boundary line, but still) is the solution region.

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Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge

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Answer:

Options A and D are correct choices.

Step-by-step explanation:

We have been given an inequality $x\leq -7$ and we are asked to find the correct options from our given choices.

Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.

(A) $3x\leq -21$

$x\leq \frac{-21}{3}$

$x\leq -7$

We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.

(B) $3x\geq -21$

$x\geq \frac{-21}{3}$

$x\geq -7$

This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.

Dividing inequality by a negative number swaps inequality sign.

$x\geq \frac{21}{-3}$

$x\geq -7$

This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.

(D) $-3x\geq 21$