Question

1. which of the following graphs shows the solution set to x - 3 > 4 and 2x - 6 ≤ 12?

Explanation:

1. First, solve the inequalities:

• Solve \(x - 3>4\):
• Add 3 to both - sides of the inequality \(x - 3>4\). Using the addition - property of inequalities, we get \(x>4 + 3\), so \(x>7\). The solution of \(x>7\) is all real numbers greater than 7, and on a number - line, it is represented by an open circle at 7 (since 7 is not included) and an arrow pointing to the right.
• Solve \(2x-6\leq12\):
• Add 6 to both sides of the inequality \(2x - 6\leq12\): \(2x\leq12 + 6\), so \(2x\leq18\).
• Divide both sides by 2: \(x\leq9\). The solution of \(x\leq9\) is all real numbers less than or equal to 9, and on a number - line, it is represented by a closed circle at 9 (since 9 is included) and an arrow pointing to the left.

1. Then, find the intersection of the two solution sets:

• The solution of the compound inequality \(x - 3>4\) and \(2x - 6\leq12\) is the set of all \(x\) such that \(7
• On a number - line, this is represented by an open circle at 7, a closed circle at 9, and a line segment connecting them.

The correct graph is the one with an open circle at 7, a closed circle at 9, and a line segment between them.

Answer:

The graph with an open circle at 7, a closed circle at 9, and a line segment connecting them.