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), the solution would include all numbers that make either of the inequalities true. This means that finding the solution set requires solving each inequality individually and then combining the results to form a comprehensive solution set.

. This means that any number greater than 3 also satisfies the inequality. Therefore, the combined solution set for the disjunction includes all numbers less than -1 or greater than 3.

Algebraic inequalities are statements that compare two expressions using inequality symbols such as '>', '<', '≥', or '≤'. To solve algebraic inequalities like those in the given exercise, you often perform the same operations you would with an equation—adding, subtracting, multiplying, or dividing both sides by the same number—with one crucial difference: when you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.

This rule is especially important and can be a common pitfall for students. When the step-by-step solution mentions flipping the inequality sign after dividing by -3, it applies this fundamental rule. Attention to this detail ensures accurate solutions to algebraic inequalities.

, the shaded region would extend to the right of 3. Since the exercise uses a disjunction (or), the final number line representation would show both regions shaded, without any intersection, as the solutions do not overlap. The number line clearly demonstrates separate intervals of valid solutions but combined present the entire solution set for the disjunction.