Question

which graph represents the solution set of the compound inequality? - 5 < a - 4 < 2

Explanation:

Step1: Solve the compound - inequality.

First, solve \(-5 < a - 4\). Add 4 to both sides: \(-5+4 < a-4 + 4\), which simplifies to \(-1 < a\). Then solve \(a - 4 < 2\). Add 4 to both sides: \(a-4 + 4<2 + 4\), which simplifies to \(a < 6\). So the solution is \(-1 < a<6\).

Step2: Analyze the graph representation.

The solution \(-1 < a<6\) is represented on a number - line with an open circle at \(-1\) (because \(a\) is greater than \(-1\) not greater than or equal to) and an open circle at 6 (because \(a\) is less than 6 not less than or equal to), and the line is shaded between \(-1\) and 6.

Answer:

The graph with an open circle at \(-1\), an open circle at 6, and the line shaded between them.