To solve the inequality \(15x - \frac{8}{10} \leq -\frac{9}{3}\), we can simplify the expressions and find the value of \(x\) that satisfies the inequality.
First, let's simplify the expression on the left side of the inequality:
\(15x - \frac{8}{10} = 15x - \frac{4}{5}\)
Next, let's simplify the expression on the right side of the inequality:
\(-\frac{9}{3} = -3\)
Now, we have the inequality:
\(15x - \frac{4}{5} \leq -3\)
To isolate the variable \(x\), we can add \(\frac{4}{5}\) to both sides:
\(15x - \frac{4}{5} + \frac{4}{5} \leq -3 + \frac{4}{5}\)
Simplifying further:
\(15x \leq -\frac{15}{5} + \frac{4}{5}\)
\(15x \leq -\frac{11}{5}\)
Finally, we can divide both sides of the inequality by 15 to solve for \(x\):
\(\frac{15x}{15} \leq \frac{-11}{5} \div \frac{15}{1}\)
\(x \leq -\frac{11}{5} \div \frac{15}{1}\)
Simplifying the division:
\(x \leq -\frac{11}{5} \times \frac{1}{15}\)
\(x \leq -\frac{11}{75}\)
Therefore, the solution to the inequality is \(x \leq -\frac{11}{75}\).