Solve this inequality: [tex]$\frac{j}{4}-8\ \textless \ 4$[/tex].
A) [tex]$j\ \textgreater \ -12$[/tex]
B) [tex]$j\ \textless \ 48$[/tex]
C) [tex]$j\ \textless \ -48$[/tex]
D) [tex]$j\ \textless \ 12$[/tex]
Answer (2)
Add 8 to both sides: 4 j < 12 .
Multiply both sides by 4: j < 48 .
The solution to the inequality is j < 48 .
Explanation
Understanding the Inequality We are given the inequality 4 j − 8 < 4 and need to solve for j . Our goal is to isolate j on one side of the inequality to find the range of values that satisfy the given condition.
Isolating the Term with j First, we add 8 to both sides of the inequality to isolate the term with j : 4 j − 8 + 8 < 4 + 8 This simplifies to: 4 j < 12
Solving for j Next, we multiply both sides of the inequality by 4 to solve for j : 4 ⋅ 4 j < 4 ⋅ 12 This simplifies to: j < 48
Identifying the Correct Option Therefore, the solution to the inequality is j < 48 . Comparing this to the given options, we see that option B matches our solution.
Examples
Imagine you're saving money, and you want to figure out how much you need to save each week to reach a certain goal. This inequality helps you determine the maximum amount you can spend each week while still ensuring you meet your savings target. For example, if you want to have less than $4 in debt at the end of the month, and you already owe $8, this inequality helps you calculate how much less than $48 you need to earn in total to meet your goal.
To solve the inequality 4 j − 8 < 4 , we first add 8 to both sides to isolate j , giving us 4 j < 12 . Next, we multiply both sides by 4, resulting in j < 48 . The correct answer is option B) j < 48 .
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