Question

Solve the following compound inequality. −2x + 11 > 31 or 7x − 4 ≥ 17 Select one: A. x < -11 or x ≥ 6 B. x < 5 or x ≥ 17 C. x ≥ 3 D. x < -10 or x ≥ 3

Answer 1

Answer:

The correct answer option is D. x < -10 or x ≥ 3.

Step-by-step explanation:

We are given the following compound inequality and we are to solve it:

$-2x + 11 > 31$ or $7x- 4 \geq 17$

Solving them to get:

$-2x+11>31$

$-2x>31-11$

$-2x>20$

$x$

x < -10

$7x-4\geq 17$

$7x\geq 17+4$

$x\geq \frac{21}{7}$

x ≥ 3

Therefore, the correct answer option is D. x < -10 or x ≥ 3.

Answer 2

Answer: OPTION D

Step-by-step explanation:

Solve for x in each inequality given in the problem, as you can see below:

$-2x+11>31$

$-2x+11>31\\-2x>31-11\\-2x>20\\x$

$7x-4\geq17\\7x\geq17+4\\7x\geq21\\x\geq3$

Finally you must make the union of both solutions obtained above.

Then for the first inequality you have:

$x$

and for the second inequality you have:

$x\geq3$

Therefore, the solution is:

$x$