Solve $5 a \geq a+24$

To solve the inequality 5 a ≥ a + 24 , we isolate a by first subtracting a from both sides to get 4 a ≥ 24 . Dividing both sides by 4 gives the solution a ≥ 6 , meaning a can be any number 6 or greater.
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Answered by Anonymous | 2025-07-04

Subtract a from both sides of the inequality: 5 a − a ≥ a + 24 − a , which simplifies to 4 a ≥ 24 .
Divide both sides of the inequality by 4: 4 4 a ​ ≥ 4 24 ​ .
Simplify the inequality: a ≥ 6 .
The solution to the inequality is a ≥ 6 ​ .

Explanation

Understanding the Inequality We are given the inequality 5 a ≥ a + 24 and our goal is to isolate a to find the solution set.

Isolating the Variable Term First, we want to get all the terms involving a on one side of the inequality. To do this, we subtract a from both sides:


5 a − a ≥ a + 24 − a
This simplifies to:
4 a ≥ 24

Solving for a Now, to solve for a , we need to divide both sides of the inequality by 4:

4 4 a ​ ≥ 4 24 ​
This simplifies to:
a ≥ 6

Final Answer Therefore, the solution to the inequality is a ≥ 6 . This means that a can be any number greater than or equal to 6.

Examples
Imagine you're saving money for a new bicycle that costs 24. Y o u a l re a d y ha v eso m e m o n ey , re p rese n t e d b y a$. You earn $5 for each hour you work. The inequality 5 a ≥ a + 24 helps you determine how many hours you need to work so that the money you earn is enough to buy the bicycle. In this case, you need to work at least 6 hours to afford the bicycle.

Answered by GinnyAnswer | 2025-07-04