Q9. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

When solving an inequality, multiplying each side by a negative number reverses the inequality symbol.

Step-by-Step Solution

Answer

The given sentence is True.

Step 1. Write the multiplication property of inequalities.

The multiplication property of inequalities states that if both sides of the inequality are multiplied by a positive number the sign of the inequality remains the same and if both sides of the inequality are multiplied by a negative number then the sign of the inequality changes that is:

(i) If $a>b$ and $c$ is a positive number then $ac>bc$.

(ii) If $a<b$ and $c$ is a positive number then $ac<bc$.

(ii) If $a>b$ and $c$ is a negative number then $ac<bc$.

(iv) If $a<b$ and $c$ is a negative number then $ac>bc$.

Step 2. State whether the given sentence is true or false.

The given sentence is true because multiplication property of inequalities states that if both sides of the inequality are multiplied by a positive number the sign of the inequality remains the same and if both sides of the inequality are multiplied by a negative number then the sign of the inequality changes.