In Exercises 25-38, solve each equation.20 - x/3=x/2

Question

Accepted Answer

Hello, today we're going to be solving the following equation. So what we are given is 18 minus X over four is equal to X over five. Now, for simplicity, we're gonna go ahead and represent 18 as a rational number and we can do that by putting it over the value of one. So now what we have is a rational equation. And in order to approach this, we can go ahead and eliminate the denominators by looking for at least common multiple of the denominators. So the question is what is the least common multiple between 14 and five? Well, in this case here, the least common multiple is going to be 20. So what we're going to do is we're going to multiply each term by 20 in order to eliminate the denominators, that is going to give us 18/1, multiplied by 20/1 minus X over four, multiplied by 20/1. And that is going to equal to X over five, multiplied by 20/1. Now, what we're going to do is we're going to go ahead and cross reduce to get rid of the denominators in the first term there's nothing further we can do to simplify. So we're going to multiply 18 and 20 together. In the second term, we have four in the, in the denominator and 20 in the numerator, both are divisible by four. And that's going to allow us to reduce the denominator to one and reduce the value of to 5. And in the last term, we have five and 20 in both the numerator and denominator, both of them are divisible by five. And that's gonna allow us to reduce these values to one and four. So what we are left with is 18 times 20 minus X times five is equal to X times four. And multiplying these values together is going to give us 360 minus five. X is equal to four X. Now, in order to solve for this equation, we're gonna go ahead and move all the X terms to the right side of the equation. So what we're going to do is we're going to add five X to both sides of the equation. And that is going to leave us with 360 equal to nine X. And finally, in order to solve for X, we're going to divide both sides of the equation by nine. And that is going to leave us with 40 is equal to X, 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 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.20 - x/3=x/2

Key Concepts

Solving Linear Equations

Combining Like Terms

Fraction Operations

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