mamushka0929
contestada

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

Respuesta :

carlosego

Answer: OPTION D

Step-by-step explanation:

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

[tex]-2x+11>31[/tex]

[tex]-2x+11>31\\-2x>31-11\\-2x>20\\x<-10[/tex]

[tex]7x-4\geq17\\7x\geq17+4\\7x\geq21\\x\geq3[/tex]

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

Then for the first inequality you have:

[tex]x<-10[/tex]

and for the second inequality you have:

[tex]x\geq3[/tex]

Therefore, the solution is:

[tex]x<-10\ or\ x\geq3[/tex]

alinakincsem

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:

[tex]-2x + 11 > 31[/tex] or [tex]7x- 4 \geq  17[/tex]

Solving them to get:

[tex]-2x+11>31[/tex]

[tex]-2x>31-11[/tex]

[tex]-2x>20[/tex]

[tex]x<-\frac{20}{2}[/tex]

x < -10

[tex]7x-4\geq 17[/tex]

[tex]7x\geq 17+4[/tex]

[tex]x\geq \frac{21}{7}[/tex]

x ≥ 3

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