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In Mathematics / College | 2025-07-04

Which step could be used to help isolate the variable in the following equation?

[tex]5.6 j-0.12=4+1.1 j[/tex]

A. Subtract 0.12 from both sides.
B. Subtract 5.6 from both sides.
C. Subtract [tex]4 j[/tex] from both sides.
D. Subtract [tex]1.1 j[/tex] from both sides.

Asked by carlos2635

Answer (1)

The goal is to isolate the variable j in the equation 5.6 j − 0.12 = 4 + 1.1 j .
Subtracting 1.1 j from both sides moves the j term from the right side to the left side.
This results in the equation 4.5 j − 0.12 = 4 .
Therefore, the correct step is to subtract 1.1 j from both sides. Subtract 1.1 j from both sides. ​

Explanation

Understanding the Problem We are given the equation 5.6 j − 0.12 = 4 + 1.1 j and asked which step helps isolate the variable j . Isolating j means getting all terms with j on one side of the equation and all constant terms on the other side.

Analyzing the Options Let's analyze the given options:



Subtract 0.12 from both sides: This would move the constant term from the left side to the right side, resulting in 5.6 j = 4.12 + 1.1 j . This is a valid step, but it doesn't directly isolate j .
Subtract 5.6 from both sides: This is not a valid operation since 5.6 is not a term in the equation. It should be 5.6j.
Subtract 4 j from both sides: This is not the term we have in the equation. We have 1.1 j on the right side, so subtracting 4 j is not helpful.
Subtract 1.1 j from both sides: This would move the j term from the right side to the left side, resulting in 5.6 j − 1.1 j − 0.12 = 4 , which simplifies to 4.5 j − 0.12 = 4 . This is a step towards isolating j .


Conclusion Subtracting 1.1 j from both sides is the most helpful step among the given options to isolate the variable j .

Examples
In physics, when analyzing motion, you might have an equation relating velocity ( v ) and time ( t ) like 3.2 t + 5 = 1.1 t + 10 . Isolating t helps you find the specific time at which two objects have the same velocity. By subtracting 1.1 t from both sides, you simplify the equation and move closer to solving for t , which is a common task in kinematics problems.

Answered by GinnyAnswer | 2025-07-04

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