In Exercises 25-38, solve each equation.(x + 3)/6 = 2/3 + (x - 5)...

Question

In Exercises 25-38, solve each equation.(x + 3)/6 = 2/3 + (x - 5)/4

Accepted Answer

Hello, today we're gonna be solving the following equation. So what we are given is X plus 1/5 is equal to 3/4 plus X minus 2/8. Now, the easiest way to approach this problem is to go ahead and eliminate the denominators. In order to do that, we're going to look for the least common multiple between the three denominators. So the question is what is going to be the least common multiple between 54 and eight? Well, in this case here, the least common multiple is going to be 40. So what we're going to do now is we're going to multiply each term in the equation by 40 in order to eliminate the denominators. So that's going to give us X plus 1/5, multiplied by 40/1. And that is going to equal to 3/4, multiplied by 40/ plus X minus 2/ multiplied by 40/1. Now, in the first term, five and 40 are both divisible by five. So we can go ahead and reduce the denominator to be one and reduce the numerator to be eight in the second term four and are both multiples of four. So we can reduce the denominator to one and reduce the numerator to 10. And in the last term, eight and 40 are both multiples of eight. That's going to reduce the denominator to one and reduce the numerator to five. So what we are left with is eight times X plus one is equal to three times 10 plus five times X minus two. Now, what we're going to do is we're going to open up the parentheses in order to do that, we're going to distribute eight into X plus one and five into X minus two and multiply three and 10 together, that is going to give us eight, X plus eight is equal to 30 plus five, X minus 10. And on the right hand side, we can go ahead and combine the constants of 30 and negative 10 together to give us positive 20. So we have eight, X plus eight is equal to 20 plus five X. Now, what we're going to do in order to solve for X is we're going to move all the X terms to the left hand side of the equation and move all the constants to the right hand side. So what we're going to do is we're going to subtract five X to both sides of the equation and we're going to subtract eight to both sides of the equation that is going to give us three X is equal to 12. And in order to solve for X, we're going to divide both sides by three and that is going to give us X is equal to four, which is going to be the solution to this equation. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 25-38, solve each equation.(x + 3)/6 = 2/3 + (x - 5)/4

Key Concepts

Rational Equations

Cross-Multiplication

Isolating the Variable

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