Question

which statement about solving inequalities is true?

subtracting the same value from both sides of an inequality changes the solution set.

adding the same value to both sides of an inequality does not change the solution set.

when dividing both sides of an inequality by the same positive value, it is necessary to reverse the inequality sign.

when multiplying both sides of an inequality by the same negative value, it is not necessary to reverse the inequality sign.

Explanation:

Analyze addition property of inequalities

Using the Inequality Properties knowledge point
Adding the same real number to both sides of an inequality produces an equivalent inequality with the exact same solution set.

$$ a < b \iff a + c < b + c $$

Evaluate the remaining options

Using the Inequality Properties knowledge point

• Subtracting the same value does not change the solution set.
• Dividing by a positive value does not reverse the inequality sign.
• Multiplying by a negative value requires reversing the inequality sign.

Answer:

• Subtracting the same value from both sides of an inequality changes the solution set.
• Adding the same value to both sides of an inequality does not change the solution set. (Correct answer)
• When dividing both sides of an inequality by the same positive value, it is necessary to reverse the inequality sign.
• When multiplying both sides of an inequality by the same negative value, it is not necessary to reverse the inequality sign.