Question

solve the inequality and graph the solution.
$20 \geq \frac{a}{6} + 19$
to draw a ray, plot an endpoint and select an arrow.
closed to open. select the middle of the ray to delete

Explanation:

Step1: Subtract 19 from both sides

To isolate the term with \( a \), we subtract 19 from both sides of the inequality \( 20 \geq \frac{a}{6} + 19 \).
\[
20 - 19 \geq \frac{a}{6} + 19 - 19
\]
Simplifying both sides, we get:
\[
1 \geq \frac{a}{6}
\]

Step2: Multiply both sides by 6

To solve for \( a \), we multiply both sides of the inequality \( 1 \geq \frac{a}{6} \) by 6.
\[
1 \times 6 \geq \frac{a}{6} \times 6
\]
Simplifying both sides, we get:
\[
6 \geq a
\]
Which can also be written as \( a \leq 6 \).

Answer:

The solution to the inequality is \( a \leq 6 \). To graph this solution:

• Plot a closed dot at \( 6 \) on the number line (since the inequality is "less than or equal to").
• Draw an arrow pointing to the left (towards negative infinity) to represent all values of \( a \) less than or equal to \( 6 \).