24) $\frac{3 x+2}{10}-\frac{1+6 x}{5} \leq-\frac{1}{2}$
Answer
Since the solution x = 5/9 satisfies the original inequality, the solution to the inequality is \(\boxed{\frac{5}{9}}\)
Step 1 ：Rewrite the inequality as \(\frac{3 x+2}{10}-\frac{2(1+6 x)}{10} \leq -\frac{1}{2}\)
Step 2 ：Combine the fractions on the left side of the inequality to get \(\frac{3 x+2-2(1+6 x)}{10} \leq -\frac{1}{2}\)
Step 3 ：Multiply both sides of the inequality by 10 to get rid of the denominator on the left side, resulting in \(3 x+2-2(1+6 x) \leq -5\)
Step 4 ：Solve the inequality for x to get x = 5/9
Step 5 ：Check if the solution x = 5/9 satisfies the original inequality
Step 6 ：Since the solution x = 5/9 satisfies the original inequality, the solution to the inequality is \(\boxed{\frac{5}{9}}\)
