Question

solve \\( \frac{5}{9}v \leq -45 \\). graph the solution. the solution is \\( \square \\).

Explanation:

Step1: Isolate the variable \( v \)

To solve the inequality \(\frac{5}{9}v \leq -45\), we multiply both sides by the reciprocal of \(\frac{5}{9}\), which is \(\frac{9}{5}\). Since \(\frac{9}{5}\) is positive, the direction of the inequality sign remains the same.

$$ v \leq -45 \times \frac{9}{5} $$

Step2: Calculate the right - hand side

First, we can simplify the multiplication: \(-45\times\frac{9}{5}=\frac{-45\times9}{5}\). We know that \(-45\div5 = - 9\), so \(-9\times9=-81\). So we get \(v\leq - 81\).

Answer:

\(v\leq - 81\)

For graphing: We would use a number line. We put a closed circle (because the inequality is "less than or equal to") at \(-81\) and draw an arrow to the left (since \(v\) is less than or equal to \(-81\)) on the number line provided (the number line has \(-81\) marked, so we place the closed circle at \(-81\) and the arrow points towards the left - hand side of the number line).