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diskwad3 diskwad3
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3 years ago
I'm struggling with the logic of the below question.



In part 'a', when you divide both sides by 'm', since 'm' is negative, shouldn't the value of 'x' change and become positive (2/m)?

In part 'b', the inequalities reverse when you multiply by 'm' on both sides.

What I'm confused about is that the logic is inconsistent. Multiplying and dividing by a negative changes the sign of the value in part 'b' but not in part 'a'.

Can someone please enlighten me on where my thinking is going wrong. Thank you.
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Staff Member
3 years ago
in part A is called "Solving Linear Equations in One Variable"  m is not negative. What happened is that since we have been asked to solve for x so we must Isolate the variable on one side of the equation.

We want to move everything except "x" (or whatever name the variable has) over to the right hand side.

on the other words, get the variable x you are solving for alone on one side and everything else on the other side using INVERSE operations.

When the variable is multiplied by a coefficient in the final stage, multiply both sides of the equation by the reciprocal of the coefficient.

in that case m is the coefficient so in order to get rid of m fromthe left side and solve for x we have to multiply the both side by 1/m (reciprocal of the coefficient) and solve for x.



in part B, we are solving for m using inequality. Solving inequalities is very like solving equations ... we do most of the same things, but we must also pay attention to the direction of the inequality.

because m is negative and we are solving for m, which means we need m to be positive. With inequality you must change the direction of the inequality when multiplying both side by negative.
diskwad3 Author
wrote...
3 years ago
Thank you for your response, but I'm still confused.

The very first line of the question states that 'm' is a negative number.

So in part A, how can 'm' not be negative when it's mentioned that it's a negative number on the 1st line of the question?

In part B, 'm' is treated as a negative number.

I don't have a problem understanding that you need to change signs and inequality directions when multiplying or dividing by a negative number in transposing an equation or inequality. That's not what I'm having trouble with.

What I'm having trouble with understanding is why 'm' is treated as negative in part B, but treated as a positive number in part A.

Or is this just a typo in the textbook that I'm working off?

I hope this clarifies my original question.
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3 years ago Edited: 3 years ago, bio_man
In part 'a', when you divide both sides by 'm', since 'm' is negative, shouldn't the value of 'x' change and become positive (2/m)?

No, that's only when dealing in inequalities. That isn't an inequality, it's just an equation, so that rule doesn't apply.

Quote
In part 'b', the inequalities reverse when you multiply by 'm' on both sides.

The solution is incorrect. That only happens when dividing or multiplying my a negative number -- the second step in the solution doesn't show that, therefore it was a typo. Therefore, the inequality should have only changed at the end. The answer is right, the process was wrong.

Let me know if you need anything else...
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