Solve each equation. 10/4x-4 = 1 /1-x

Question

Accepted Answer

Hello, everyone in this video, we're going to be looking at this practice problem where we want to solve for X in the equation divided by 37 X minus 74 equal to one divided by two minus X. So in this case, you can see that I have X on both the left hand side and the right hand side. And in order to solve for X, I want to try to isolate X on one side. And in order to start doing that, I need to get it out of the denominator. And if we look at 37 X minus 74 X, I can actually pull out the 37. So now I have 25 divided by 37 times x and 74 divided by 37 is two and that is equal to one divided by two minus X. So now you can see that these denominators look very familiar except that the signs are switched. So I'm actually going to pull out a negative from my right hand side. So that leaves me with negative two plus eight. And if I rewrite it, I can say this is negative one over X -2. And my Left hand side is still 25 divided by times X -2. And now you can say you have X -2 -2 In both denominators. So in order to cancel them, I'll multiply both sides by X -2. And because I did it to both sides, You can see that X -2 gets canceled from both denominators. So that leaves me with 25 divided by 37 is equal to negative one. And this statement is not true, which means that for this equation, there is no solutions for X that would make the equation true. So that becomes my final answer. And if you look answer, choice, D also states that there's no solution for this equation. So hopefully this video helped and see you next time.

Solve each equation. 10/4x-4 = 1 /1-x

Key Concepts

Algebraic Equations

Rational Expressions

Cross-Multiplication

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