Question

solve the inequality and graph the solution.
2(d + 1) - 5 > 3
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Simplify the left side

Use the distributive property \(a(b + c)=ab+ac\).
\(2(d + 1)-5=2d+2 - 5=2d-3\).
The inequality becomes \(2d-3>3\).

Step2: Isolate the term with \(d\)

Add \(3\) to both sides of the inequality.
By the addition - property of inequalities \(a>b\Rightarrow a + c>b + c\).
\(2d-3+3>3 + 3\), which simplifies to \(2d>6\).

Step3: Solve for \(d\)

Divide both sides by \(2\).
By the division - property of inequalities \(a>b,c>0\Rightarrow\frac{a}{c}>\frac{b}{c}\).
\(\frac{2d}{2}>\frac{6}{2}\), so \(d > 3\).

Answer:

The solution of the inequality \(2(d + 1)-5>3\) is \(d>3\). On the number - line, we have an open circle at \(d = 3\) (because \(d = 3\) is not included in the solution set) and a ray extending to the right of \(3\).