Solve the inequality.
[tex]$-95+6 x \geq 42.1$[/tex]
Answer (2)
Add 95 to both sides: 6 x ≥ 137.1 .
Divide both sides by 6: x ≥ 6 137.1 .
Simplify the fraction: x ≥ 22.85 .
The solution to the inequality is: x ≥ 22.85 .
Explanation
Understanding the Inequality We are given the inequality − 95 + 6 x ≥ 42.1 . Our goal is to isolate x on one side of the inequality to find the solution.
Adding to Both Sides To begin, we add 95 to both sides of the inequality to eliminate the -95 term on the left side: − 95 + 6 x + 95 ≥ 42.1 + 95
Simplifying the Inequality Simplifying both sides, we get: 6 x ≥ 137.1
Dividing to Isolate x Next, we divide both sides of the inequality by 6 to solve for x : 6 6 x ≥ 6 137.1
Finding the Solution Performing the division, we find: x ≥ 22.85
Examples
Imagine you're saving money for a new bicycle that costs $42.1. You start with a debt of $95, but you earn $6 every hour. The inequality helps you determine how many hours you need to work to not only pay off your debt but also afford the bicycle. Understanding inequalities is crucial for managing finances and planning expenses effectively.
To solve the inequality − 95 + 6 x ≥ 42.1 , we first add 95 to both sides to obtain 6 x ≥ 137.1 . Then, we divide both sides by 6, yielding x ≥ 22.85 . Thus, the solution to the inequality is x ≥ 22.85 .
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