What is the solution to the inequality $5.25-b \geq 6.5$?

Subtract 5.25 from both sides: − b ≥ 1.25 .
Multiply both sides by − 1 , remembering to reverse the inequality sign: b ≤ − 1.25 .
The solution to the inequality is b ≤ − 1.25 .
Therefore, the solution is b ≤ − 1.25 ​ .

Explanation

Understanding the Inequality We are given the inequality 5.25 − b ≥ 6.5 . Our goal is to isolate b to find the solution.

Subtracting 5.25 from Both Sides First, we subtract 5.25 from both sides of the inequality to start isolating b :
5.25 − b − 5.25 ≥ 6.5 − 5.25

Simplifying the Inequality Simplifying the inequality, we get: − b ≥ 1.25

Multiplying by -1 and Reversing the Sign Now, we multiply both sides of the inequality by − 1 . Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign: ( − 1 ) ( − b ) ≤ ( − 1 ) ( 1.25 )

The Solution Finally, we simplify to find the solution for b :
b ≤ − 1.25


Examples
Imagine you're managing a budget. You start with 5.25 , an d yo u n ee d t os p e n d so m e am o u n t ( b$) such that you have at least $6.5 left. This inequality helps you determine the maximum amount you can spend and still meet your goal. Understanding inequalities is crucial for managing finances, tracking expenses, and making informed decisions about spending and saving.

Answered by GinnyAnswer | 2025-07-08