Question

2 graph the solution set of \\(\frac{a}{2} + 5 > 4\\). show your work.

Explanation:

Step1: Solve the inequality

Subtract 5 from both sides of the inequality $\frac{a}{2}+5 > 4$.
We get $\frac{a}{2}+5 - 5>4 - 5$, which simplifies to $\frac{a}{2}>- 1$.

Step2: Isolate the variable \(a\)

Multiply both sides of the inequality $\frac{a}{2}>-1$ by 2.
We have $2\times\frac{a}{2}>2\times(-1)$, so \(a > - 2\).

Step3: Graph the solution

To graph \(a > - 2\) on a number line:

• Draw a number line.
• Locate the point \(-2\) on the number line.
• Since the inequality is \(a > - 2\) (not \(a\geq - 2\)), we use an open circle at \(-2\) to indicate that \(-2\) is not included in the solution set.
• Then, draw an arrow to the right of \(-2\) to show all the numbers greater than \(-2\) are in the solution set.

Answer:

The solution to the inequality is \(a > - 2\), and its graph has an open circle at \(-2\) with an arrow pointing to the right.