Question

For which of the following inequalities, is -4 part of the solution set? Select all that apply. A. x > -5 . B. 2 > X . C. 3x + 4 > -8 D. 5x < 2x - 3 E. ---6 < 4 - 2x​

Answer 1

$-4$ is a part of the solution set to all of the inequalities

We will consider each inequality in turn:

For $x>-5$:

The solution set is $\{{-4,-3,-2,-1,...\}$

So $-4$ is a part of the solution set of $x>-5$

For $2>x$, or $x<2$:

The solution set is $\{{1,0-1,-2,-3,-4,...\}$

So $-4$ is a part of the solution set of $2>x$

For $3x+4\ge -8$:

We have to solve first

$3x+4\ge -8\\3x\ge -8-4\\3x\ge -12\\x\ge -4$

The solution set is $\{{-4,-3,-2,-1,0,...\}$

So $-4$ is a part of the solution set of $3x+4\ge -8$

For $5x\le 2x-3$:

We have to solve first

$5x\le 2x-3\\5x-2x\le-3\\3x\le-3\\x\le-1$

The solution set is $\{{-1,-2,-3,-4,-5,...\}$

So $-4$ is a part of the solution set of $5x\le 2x-3$

For $-6<4-2x$:

We have to solve first

$-6<4-2x\\2x<4+6\\2x<10\\x<5$

The solution set is $\{{4,3,2,...,-3,-4,-5,...\}$

So $-4$ is a part of the solution set of $-6<4-2x$

So, $-4$ is a part of the solution set of all the inequalities.

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