Question

1. solve the inequality and graph its solution.

\\( \frac{4a}{6} < -52 \\)

Explanation:

Step1: Multiply both sides by 6

To eliminate the denominator, multiply both sides of the inequality \(\frac{4a}{6} < -52\) by 6. This gives \(4a < -52\times6\). Calculating \(-52\times6\), we get \(4a < -312\).

Step2: Divide both sides by 4

Now, divide both sides of the inequality \(4a < -312\) by 4 to solve for \(a\). So, \(a < \frac{-312}{4}\), which simplifies to \(a < -78\).

(For graphing: On a number line, we draw an open circle at -78 (since the inequality is strict, \(a < -78\) not \(a \leq -78\)) and shade the region to the left of -78 to represent all values of \(a\) that satisfy the inequality.)

Answer:

The solution to the inequality is \(a < -78\)