Solve the inequality for $v$.
$10 \geq v+14$
Answer (1)
Subtract 14 from both sides of the inequality: 10 − 14 ≥ v + 14 − 14 .
Simplify the inequality: − 4 ≥ v .
Rewrite the inequality to solve for v : v ≤ − 4 .
The solution to the inequality is v ≤ − 4 .
Explanation
Understanding the Inequality We are given the inequality 10 ≥ v + 14 . Our goal is to isolate v on one side of the inequality to solve for it.
Subtracting 14 from Both Sides To isolate v , we need to subtract 14 from both sides of the inequality. This maintains the balance of the inequality. So we have: 10 − 14 ≥ v + 14 − 14
Simplifying the Inequality Now, we simplify both sides of the inequality: − 4 ≥ v
Rewriting the Inequality This inequality states that -4 is greater than or equal to v . We can rewrite this as: v ≤ − 4
Final Answer Therefore, the solution to the inequality is v ≤ − 4 . This means that v can be any value less than or equal to -4.
Examples
Imagine you're saving money for a new video game that costs $14. You currently have $10. The inequality 10 ≥ v + 14 can represent how much more money you can 'owe' (represented by a negative number) to still be able to buy the game once you get your next allowance. Solving this inequality tells you the maximum amount you can borrow (or be in debt) and still afford the game.
