Solve this inequality: $3 b-7<32$
Answer (1)
Add 7 to both sides of the inequality: 3 b < 39 .
Divide both sides by 3: b < 13 .
The solution to the inequality is b < 13 .
The correct option is B: b < 13 .
Explanation
Understanding the Inequality We are given the inequality 3 b − 7 < 32 . Our goal is to isolate b to find the solution set.
Adding 7 to Both Sides First, we add 7 to both sides of the inequality to get rid of the -7 on the left side: 3 b − 7 + 7 < 32 + 7
Simplifying the Inequality This simplifies to: 3 b < 39
Dividing by 3 Next, we divide both sides of the inequality by 3 to isolate b :
3 3 b < 3 39
Final Solution This simplifies to: b < 13
Selecting the Correct Option Therefore, the solution to the inequality is b < 13 . Comparing this to the given options, we see that option B is the correct answer.
Examples
Imagine you're saving up for a new video game that costs $32. You already have $7 saved, and you plan to save $3 each week. The inequality 3 b − 7 < 32 helps you determine how many weeks ( b ) it will take to have less than $32 saved, meaning you still can't buy the game yet. Solving this inequality shows you the number of weeks you need to save before you reach your goal. Understanding and solving inequalities like this can help you manage your savings and plan your purchases effectively.
