Question

solve the following compound inequality. write the solution set using interval notation and graph it.
2 - x < 17 + 2x or 7x + 18 > x
select the correct choice below, and fill in the answer box if necessary.
a. the solution set is (-5,∞). (type your answer in interval notation. use integers or fractions for any numbers in the expression.)
b. the solution set is ∅.
choose the correct graph below.

Explanation:

Step1: Solve the first inequality

Solve \(2 - x<17 + 2x\).
Add \(x\) to both sides: \(2<17 + 3x\).
Subtract 17 from both sides: \(- 15<3x\).
Divide both sides by 3: \(-5 < x\).

Step2: Solve the second inequality

Solve \(7x + 18>x\).
Subtract \(x\) from both sides: \(6x+18 > 0\).
Subtract 18 from both sides: \(6x>-18\).
Divide both sides by 6: \(x > - 3\).
Since it is an "or" compound - inequality, the solution set is the union of the solution sets of the two inequalities. The overall solution set is \(x>-5\), which in interval notation is \((-5,\infty)\).

Step3: Graph the solution

The graph of the solution set \((-5,\infty)\) has an open - circle at \(-5\) (because \(-5\) is not included in the solution set) and an arrow pointing to the right.

Answer:

A. The solution set is \((-5,\infty)\)
The correct graph is A (an open - circle at \(-5\) and an arrow pointing to the right).