Question

solve the inequality and graph the solution.
\\(\frac{a}{6} - 24 < -25\\)
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.
<----|----|----|----|----|----|----|----|----|----|--->
-10 -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Add 24 to both sides

To isolate the term with \( a \), we add 24 to both sides of the inequality \(\frac{a}{6}-24 < -25\). This gives \(\frac{a}{6}-24 + 24< -25 + 24\), which simplifies to \(\frac{a}{6}< -1\).

Step2: Multiply both sides by 6

To solve for \( a \), we multiply both sides of the inequality \(\frac{a}{6}< -1\) by 6. This gives \(\frac{a}{6}\times6< -1\times6\), which simplifies to \(a < -6\).

Answer:

The solution to the inequality is \(a < -6\). To graph this, we draw an open circle at \(-6\) (since the inequality is strict, \(a
eq -6\)) and draw a ray to the left of \(-6\) on the number line.