Question

1. which of the graphs below represents the soltuion set for d - 4 > -3?

Explanation:

Step1: Solve the inequality

Given \(d - 4> - 3\). Add \(4\) to both sides of the inequality. Using the addition property of inequalities \(a>b\Rightarrow a + c>b + c\).
\(d-4 + 4>-3 + 4\)
\(d>1\)

Step2: Analyze the number - line representation

For the inequality \(d>1\), on a number - line:

• There is an open circle at \(d = 1\) (because \(d = 1\) is not included in the solution set, since the inequality is strict, \(d>1\) not \(d\geq1\)).
• The line extends to the right of \(1\) (because all values greater than \(1\) satisfy the inequality).

Looking at the options:

• The first option has the open - circle at \(7\) (incorrect).
• The second option has the open - circle at \(- 6\) (incorrect).
• The third option has the open - circle at \(0\) (incorrect).
• The fourth option has the open - circle at \(1\) and the line extending to the right (correct).

Answer:

The fourth graph (the one with an open circle at \(1\) and the line extending to the right) represents the solution set for \(d - 4>-3\).