Question

consider the following compound inequality. (\frac{18}{4} < \frac{y + 5}{2} < \frac{29}{4}) step 2 of 2: graph the solution set. answer how to enter your answer (opens in new window) keypad keyboard shortcuts previous step answer pressing the buttons will create an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed intervals, use the clear button. to indicate infinity or negative infinity, drag an open end point to the end of the number line. (-infty -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 infty)

Explanation:

Step1: Solve the left inequality

First, solve \(\frac{18}{4}<\frac{y + 5}{2}\). Multiply both sides by 2 (since 2 is positive, the inequality sign remains the same):
\(2\times\frac{18}{4}Simplify \(\frac{36}{4}Subtract 5 from both sides: \(9-5

Step2: Solve the right inequality

Next, solve \(\frac{y + 5}{2}<\frac{29}{4}\). Multiply both sides by 2:
\(y + 5<\frac{29}{4}\times2\)
Simplify \(\frac{58}{4}\) to \(\frac{29}{2}=14.5\), so \(y + 5<14.5\).
Subtract 5 from both sides: \(y<14.5 - 5\), which gives \(y<9.5\) or \(y<\frac{19}{2}\).

Step3: Combine the solutions

From the two inequalities, we have \(4

Answer:

The solution set is the open interval \((4,\frac{19}{2})\) (or \((4, 9.5)\)). When graphing, place open circles at 4 and \(9.5\) on the number line and draw a line segment connecting them.