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WRITINGTo solve $3 x-4=5 x+1,$ one student began by subtracting $3 x$ from both sides. Another student solved the same equation by first subtracting $5 x$ from both sides. Will the students get the same solution? Explain why or why not.
yes
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 2
More about Solving Equations
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Missouri State University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
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00:19
Reasoning when solving $\f…
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Solve equation and check y…
Solve the equation by cros…
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Solve equation. Be sure to…
01:07
Solve.$$\frac{5}{3 x-4…
00:52
Is $\frac{3}{4}$ a solutio…
00:40
Solve each equation, and c…
01:41
Solve the equation.$$<…
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A student attempted to sol…
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we have these two students who are both solving three X minus four equals five X plus one and student one began by subtracting three extra both sides. So they did. This student to, on the other hand, started by subtracting the five X from both sides. So instead of doing what student one did, they did this. So the question is, are they both going to arrive at the same answer? And so I want you to think about what's gonna happen. Let's go back to student one. We end up with negative four equals two X plus one, and student to we would end up with negative two X minus four equals one. So I want to think about what the next step would would be. So on either side you would move the integers to the other side. We're gonna end up with same thing. It's just that one student has a positive to X or student. One has a positive to X, and student, too has a negative to X. When they go about solving, they're still going to get the same value for X. They're just working on opposite values. So yes, same solutions just reverse operations. Okay? They're still going to get there. I'll just go get there a slightly different way where this student will end up having to divide by a negative. And this student will already have a negative in play when they divide by a positive.
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