Question

question 2 of 12, step 2 of 2
correct
consider the following compound inequality.
{ x | 2 x + 2 < - 4 or 7 > - 5 x - 3 }
step 2 of 2 : graph the solution to the given compound inequality.
keypad
opens in new window)
keypad
keyboard shortcuts
previous step answer
ate an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed
on. to indicate infinity or negative infinity, drag an open end point to the end of the number line.

Explanation:

Step 1: Solve the first inequality \(2x + 2<-4\)

Subtract 2 from both sides:
\(2x+2 - 2<-4 - 2\)
\(2x<-6\)
Divide both sides by 2:
\(x < - 3\)

Step 2: Solve the second inequality \(7>-5x - 3\)

Add 3 to both sides:
\(7 + 3>-5x-3 + 3\)
\(10>-5x\)
Divide both sides by \(-5\) and reverse the inequality sign:
\(x>-2\)

The solution of the compound inequality \(\{x|2x + 2 < - 4\) or \(7>-5x - 3\}\) is \(x < - 3\) or \(x>-2\)

Answer:

Graph an open - circle at \(x = - 3\) and shade to the left (for \(x < - 3\)), and graph an open - circle at \(x=-2\) and shade to the right (for \(x > - 2\))