Question
What property of inequality justifies the steps shown in the following solution process 2/5x is less than or equal to negative 10 is it addition property division property multiplication or subtraction
Answers
GPT-4o mini
To determine which property of inequality justifies the steps shown in solving \( \frac{2}{5}x \leq -10 \), let's first transform the inequality by isolating \( x \).
1. **Multiply both sides by the reciprocal of \( \frac{2}{5} \)**, which is \( \frac{5}{2} \).
\[ \frac{5}{2} \cdot \frac{2}{5} x \leq -10 \cdot \frac{5}{2} \]
2. This simplification yields:
\[ x \leq -25 \]
The operation of multiplying both sides of the inequality by \( \frac{5}{2} \) uses the **Multiplication Property of Inequalities**, which states that if you multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.
So, the answer is **Multiplication Property**.
1. **Multiply both sides by the reciprocal of \( \frac{2}{5} \)**, which is \( \frac{5}{2} \).
\[ \frac{5}{2} \cdot \frac{2}{5} x \leq -10 \cdot \frac{5}{2} \]
2. This simplification yields:
\[ x \leq -25 \]
The operation of multiplying both sides of the inequality by \( \frac{5}{2} \) uses the **Multiplication Property of Inequalities**, which states that if you multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.
So, the answer is **Multiplication Property**.