To solve the inequality \( 14 \geq -2(a - 10) \), we will first simplify the expression on the right side.
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Distribute the \(-2\) on the right side: \[ 14 \geq -2a + 20 \]
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Next, we can isolate \(a\) by subtracting \(20\) from both sides: \[ 14 - 20 \geq -2a \quad \Rightarrow \quad -6 \geq -2a \]
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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:
- Plot a closed circle (filled) at \(3\).
- 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.