What is the solution to this inequality?
$\frac{x}{10}+6 \geq 8$
A. $x \geq 20$
B. $x \leq 74$
C. $x \leq 20$
D. $x \geq 74$
Answer (1)
Subtract 6 from both sides: 10 x ≥ 2 .
Multiply both sides by 10: x ≥ 20 .
The solution to the inequality is x ≥ 20 .
The final answer is x ≥ 20 .
Explanation
Understanding the Inequality We are given the inequality 10 x + 6 ≥ 8 . Our goal is to isolate x to find the solution set.
Subtracting 6 from Both Sides First, we subtract 6 from both sides of the inequality to isolate the term with x : 10 x + 6 − 6 ≥ 8 − 6 10 x ≥ 2
Multiplying by 10 Next, we multiply both sides of the inequality by 10 to solve for x : 10 × 10 x ≥ 10 × 2 x ≥ 20
Final Solution Therefore, the solution to the inequality is x ≥ 20 .
Examples
Imagine you're saving money for a new video game that costs $80. You've already saved $60, and each week you save an additional tenth of your target amount. This inequality helps you determine how many weeks you need to save to reach your goal. Understanding and solving inequalities is crucial in managing budgets, tracking progress, and making informed financial decisions.
