Which represents the solution set of the inequality [tex]$5 x-9 \leq 21$[/tex]?

A. [tex]$x \leq \frac{12}{5}$[/tex]
B. [tex]$x \geq \frac{12}{5}$[/tex]
C. [tex]$x \geq 6$[/tex]
D. [tex]$x \leq 6$[/tex]

The solution set of the inequality 5 x − 9 ≤ 21 is x ≤ 6 . The correct option is D. x ≤ 6 .
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Answered by Anonymous | 2025-07-04

Add 9 to both sides of the inequality: 5 x − 9 + 9 ≤ 21 + 9 , which simplifies to 5 x ≤ 30 .
Divide both sides by 5: 5 5 x ​ ≤ 5 30 ​ .
Simplify to find the solution: x ≤ 6 .
The solution set of the inequality is x ≤ 6 ​ .

Explanation

Understanding the Inequality We are given the inequality 5 x − 9 ≤ 21 . Our goal is to isolate x on one side of the inequality to find the solution set.

Adding 9 to Both Sides First, we add 9 to both sides of the inequality to eliminate the -9 on the left side: 5 x − 9 + 9 ≤ 21 + 9 This simplifies to: 5 x ≤ 30

Dividing by 5 Next, we divide both sides of the inequality by 5 to solve for x :
5 5 x ​ ≤ 5 30 ​ This simplifies to: x ≤ 6

Final Solution Therefore, the solution set for the inequality 5 x − 9 ≤ 21 is x ≤ 6 .


Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, when budgeting, you might have an inequality that represents the maximum amount you can spend each month. If you have $500 available for expenses and $200 is allocated for rent, the inequality x + 200 ≤ 500 represents the amount x you can spend on other things. Solving this inequality tells you the maximum you can spend without exceeding your budget. Similarly, in science, inequalities can define acceptable ranges for experimental conditions, ensuring results are valid and safe.

Answered by GinnyAnswer | 2025-07-04