In Exercises 25-38, solve each equation.3x/5 = 2x/3 +1

Question

Accepted Answer

Hello, today we're going to be solving the following equation. So what we are given is seven X over 12 is equal to two X over three plus two. Now, for simplicity, we're gonna go ahead and represent two as a rational number and we're gonna do that by putting it over one. So the easiest way to approach this rational equation is to go ahead and find a least common multiple between the three numbers. That way we can multiply each term by the lowest common multiple and eliminate the denominators. So the question is what is the least common multiple between 12, 3 and one? Well, in this case here, the least common multiple is going to be 12. So what we're going to do is we're going to multiply each term of the equation by 12 in order to eliminate the denominators, that is going to give us seven X over 12, multiplied by 12/1. And that is going to equal to two X over three, multiplied by 12/1 plus 2/1, multiplied by 12/1. So now what we're going to do is we're going to cross reduce in the first term, we have 12 in both the numerator and denominator. Therefore, we can just go ahead and cancel out those values. In the second term, three and 12 are multiples of three. So we can divide both of those values by three to reduce the denominator to one and reduce do 12 to 4. And in the third term, there's nothing further we can do. So we're just gonna multiply twe two and 12 together. This is going to leave us with seven X is equal to four times two, X plus two times 12. And multiplying the values together is going to give us seven X is equal to eight X plus 24. Now, in order to solve for X, we're going to move all the X terms to one side of the equation. And we're gonna do that by subtracting eight X to both sides of the equation. That is going to leave us with negative X is equal to 24. And in order to solve for X, we're going to divide both sides of the equation by negative one. And that is going to give us X is equal to negative which is going to be the solution to this given equation. And with that being said, the answer to this problem is going to be C So I hope this video helps you in understanding on 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.3x/5 = 2x/3 +1

Key Concepts

Solving Linear Equations

Fraction Operations

Combining Like Terms

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