Question

Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge 21.$ Enter the letters of all the conclusions that are correct. For example, if you think that conclusions B and D are correct, enter "B, D".

Answer 1

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.

(C) $-3x\leq 21$

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) $-3x\geq 21$  

Dividing inequality by a negative number swaps inequality sign.

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

$x\leq -7$

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