Translate "6 more than $k$ exceeds 25" to an inequality and then solve.
A. $k \geq 19$
B. $k<19$
C. $k>19$
D. $k \leq 19$
Answer (2)
Translate the statement into an inequality: 25"> k + 6 > 25 .
Subtract 6 from both sides: 25 - 6"> k > 25 − 6 .
Simplify the inequality: 19"> k > 19 .
The solution is 19"> k > 19 , meaning k is any number greater than 19. 19}"> k > 19
Explanation
Understanding the Problem The problem states "6 more than k exceeds 25". We need to translate this statement into a mathematical inequality and then solve it for k .
Translating to an Inequality "6 more than k " can be written as k + 6 . The word "exceeds" means "is greater than", so we can write the inequality as: 25"> k + 6 > 25
Isolating k To solve for k , we need to isolate k on one side of the inequality. We can do this by subtracting 6 from both sides of the inequality: 25 - 6"> k + 6 − 6 > 25 − 6
Solving for k Simplifying the inequality, we get: 19"> k > 19 So, k must be greater than 19.
Final Answer The solution to the inequality is 19"> k > 19 .
Examples
Imagine you're saving up for a new bicycle that costs $25. You already have 6 s a v e d . T h e in e q u a l i t y k + 6 > 25 h e lp syo u d e t er min e h o w m u c hm ore m o n ey ( k$) you need to save to exceed the bicycle's price. Solving it tells you that you need to save more than $19 to afford the bicycle.
The inequality for the statement "6 more than k exceeds 25" is 25"> k + 6 > 25 , which simplifies to 19"> k > 19 . Therefore, the correct answer is option C.
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