Solve $-\frac{x}{3} \geq 5$.
A. $x \geq 15$
B. $x \leq-15$
C. $x \geq-15$
D. $x \leq 15$
Answer (1)
Multiply both sides of the inequality − 3 x ≥ 5 by − 3 .
Remember to flip the inequality sign when multiplying by a negative number.
Simplify the inequality to get x ≤ − 15 .
The solution to the inequality is x ≤ − 15 .
Explanation
Understanding the Inequality We are given the inequality − 3 x ≥ 5 . Our goal is to isolate x to find the solution.
Multiplying by -3 To isolate x , we need to multiply both sides of the inequality by − 3 . Remember that when we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality sign.
Simplifying the Inequality Multiplying both sides by − 3 , we get:
( − 3 x ) × ( − 3 ) ≤ 5 × ( − 3 )
Simplifying, we have:
x ≤ − 15
Final Answer Therefore, the solution to the inequality is x ≤ − 15 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, consider a budget constraint where you have a maximum amount of money to spend. If you want to buy multiple items, the total cost must be less than or equal to your budget. Similarly, in physics, inequalities can describe the range of possible values for variables like speed or temperature. In economics, inequalities are used to model supply and demand curves, determining equilibrium prices and quantities. These applications highlight the importance of mastering inequalities for problem-solving in various fields.
