Solve the inequality and graph the solution.

Question

14≥
–
2(a–10)
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.

Answer 1

To solve the inequality \( 14 \geq -2(a - 10) \), we will first simplify the expression on the right side.

1. Distribute the \(-2\) on the right side: \[ 14 \geq -2a + 20 \]

2. Next, we can isolate \(a\) by subtracting \(20\) from both sides: \[ 14 - 20 \geq -2a \quad \Rightarrow \quad -6 \geq -2a \]

3. Now divide both sides by \(-2\). Remember that dividing by a negative number flips the inequality sign: \[ \frac{-6}{-2} \leq a \quad \Rightarrow \quad 3 \leq a \] or equivalently, \[ a \geq 3 \]

The solution to the inequality is \( a \geq 3 \).

Graphing the Solution:

• The endpoint is \(3\).
• Since \(3\) is included in the solution (because the inequality is \(\geq\)), we will plot it as a closed circle.
• Since the solution indicates all values greater than or equal to \(3\), we will draw a solid line (or ray) extending to the right from \(3\).

Steps to Graph:

1. Plot a closed circle (filled) at \(3\).
2. Draw a ray extending to the right from \(3\).

Thus, the graph represents all values of \(a\) that are greater than or equal to \(3\). The final graph would look like this:

<---o========================>
    3

Where "o" is a closed circle at \(3\) and "=" indicates the ray extending to the right.