Complete the statement describing the solution set to this compound inequality 3 - 2 \geqslant 11 \: or \: x + 6 \ \textgreater \ 14The solution set includes all values of X tha…

Question

complete the statement describing the solution set to this compound inequality
`3 - 2 \geqslant 11 \: or \: x + 6 \ \textgreater \ 14`The solution set includes all values of X that are ________ or _________.(first line)A. no more than -7B. at least -4C at least -7D no more than -4(second line)A. Less than 8B. greater than 20C. less than 20D. greater than 8

Answer 1

Option D is correct for the first line.

Option D is correct for the second line.

x ≤ -4

or

x > 8

Step-by-step explanation

The system of equations to be solved is

3 - 2x ≥ 11

or

x + 6 > 14

The key to solving this is to solve each pair of the equation, one at a time

3 - 2x ≥ 11

Subtract 3 from both sides

3 - 3 - 2x ≥ 11 - 3

-2x ≥ 8

Divide both sides by -2 (Note that dividing both sides of an inequality equation by a negative number changes the inequality sign)

(-2x/-2) ≤ (8/-2)

x ≤ -4

x + 6 > 14

Subtract 6 from both sides

x + 6 - 6 > 14 - 6

x > 8

So, the two solutions are

x ≤ -4 or x > 8

In statement form,

x ≤ -4 means x cannot be more than -4.

x > 8 means that x is greater than 8.

Hope this Helps!!!