Question

The solution set for the inequality x + 4 (x - 3) includes -11 as an element. true or False?

Answer 1

It depends on what is between the `x+4` and the `(x-3)`. The inequality sign isn't showing up.

Answer 2

x + 4>*or equal to* 1/2

Answer 3

1/2 is on the right side? not x-3 ?

Answer 4

1/2 on the left with (x+4)

Answer 5

can you post a screenshot of the entire problem?

Answer 6

The solution set for the inequality x + 4>*or equal to* 1/2 (x - 3) includes -11 as an element.

Answer 7

So the inequality is this right?
\[\Large x+4 \ge \frac{1}{2}(x-3)\]

Answer 8

I'm going to assume it is

Answer 9

Replace EVERY copy of 'x' with -11. Then simplify


\[\Large x+4 \ge \frac{1}{2}(x-3)\]
\[\Large -11+4 \ge \frac{1}{2}(-11-3)\]
\[\Large -7 \ge \frac{1}{2}(-14)\]
\[\Large -7 \ge -7\]

Since
\[\Large -7 \ge -7\]
is a true inequality, this means the original inequality is true when x = -11. So -11 is definitely an element of the solution set.