Solve $b-2.7 \geq 5.24$.
A) $b \leq 7.62$
B) $b \geq 7.81$
C) $b \leq 7.39$
D) $b \geq 7.94$
Answer (2)
Add 2.7 to both sides of the inequality: b − 2.7 + 2.7 ≥ 5.24 + 2.7 .
Simplify the inequality: b ≥ 5.24 + 2.7 .
Calculate the sum: 5.24 + 2.7 = 7.94 .
The solution to the inequality is: b ≥ 7.94 .
Explanation
Understanding the Inequality We are given the inequality b − 2.7 ≥ 5.24 and asked to solve for b . This means we want to isolate b on one side of the inequality.
Isolating b To isolate b , we need to add 2.7 to both sides of the inequality: b − 2.7 + 2.7 ≥ 5.24 + 2.7
Simplifying the Inequality This simplifies to: b ≥ 5.24 + 2.7 Now we need to calculate the sum 5.24 + 2.7 .
Calculating the Sum Adding the numbers, we get: 5.24 + 2.7 = 7.94 So the inequality becomes: b ≥ 7.94
Finding the Correct Option Comparing our result b ≥ 7.94 with the given options, we see that option D matches our solution.
Examples
Imagine you're saving money to buy a new video game that costs $5.24. However, you already owe your friend $2.7. The inequality helps you determine the minimum amount of money you need to have in total so that after paying your friend, you still have enough to buy the video game. Solving this inequality ensures you know the minimum savings required to achieve your goal.
To solve the inequality b − 2.7 ≥ 5.24 , we isolate b and find that b ≥ 7.94 . Therefore, the correct answer from the multiple choice options is D. This result shows the minimum value for b to satisfy the inequality.
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