$$ 5 x-2 \leq-22 $$ or $$ -3 x-24 $$

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$$ 5 x-2 \leq-22 $$ or $$ -3 x-2>4 $$

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To solve the compound inequality $$ 5x - 2 \leq -22 $$ or $$ -3x - 2 > 4 $$, we will solve each inequality separately. ### Solving the first inequality: 1. Start with the inequality: $$ 5x - 2 \leq -22 $$ 2. Add 2 to both sides: $$ 5x \leq -20 $$ 3. Divide both sides by 5: $$ x \leq -4 $$ ### Solving the second inequality: 1. Start with the inequality: $$ -3x - 2 > 4 $$ 2. Add 2 to both sides: $$ -3x > 6 $$ 3. Divide both sides by -3 (remember to reverse the inequality sign): $$ x < -2 $$ ### Combining the results: The solution to the compound inequality $$ 5x - 2 \leq -22 $$ or $$ -3x - 2 > 4 $$ is: $$ x \leq -4 \quad \text{or} \quad x < -2 $$ Since $$ x \leq -4 $$ is a more restrictive condition than $$ x < -2 $$, the final solution can be expressed as: $$ x \leq -4 $$ Thus, the solution set is: $$ \boxed{(-\infty, -4]} $$ The solution is $$ x \leq -4 $$.

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