Solve the following equations with fractions. x 4 − 2 3 = x 6 \frac{x}{4}-\frac23=\frac{x}{6}

Welcome to the practice. In this problem, we'd like to solve the equation x over four minus two thirds equals x over six. What makes this equation look a bit intimidating is that we have two fractions with an x in the numerator, x over four and x over six. So it doesn't really look like the one that we solved in the concept video. That means we should start by rewriting those two terms so that we can make the equation look a bit friendlier. So let's start with x over four. We know that x is equal to one x and that four is equal to four times one. So we can rewrite this as one x over four times one, which shows us how we can break up this fraction into one fourth times x over one. Now x over one is just x, so we can write this as one fourth x. And we can say that x over four is equal to one fourth x. We can do the same thing with x over six. Take a second, pause the video, follow the same steps, and you'll see that x over six is really just one sixth x. So we can rewrite this equation to be one fourth x minus two thirds is equal to one sixth x. And now we have it in the same form as the one that we solved in the concept video, so we're ready to follow our steps here to solve the equation, starting with step zero, which is clearing our fractions by multiplying by the least common denominator. So we wanna find the least common denominator of one fourth, minus two thirds, and one sixth. This means that we need to find the least common multiple of denominators four, three, and six, and that least common denominator is going to be 12. So let's multiply both sides of our equation by 12. That's gonna get us 12 times one fourth x minus two thirds is equal to 12 times one sixth x. And now we just need to distribute that 12. On the left, we end up getting 12 times one fourth x. Now, 12 times one fourth is three, so that's three x, and 12 times minus two thirds. 12 times two is 24, so this will get us minus 24 thirds. But because 24 divided by three is just eight, minus 24 thirds is really just minus eight. On the right side, we have 12 times one sixth x. Now 12 times one sixth is two, so this is just two x. Now we have no more fractions or decimals, so step zero is all set, and we would move on to step one. We don't have any parentheses or things we have to distribute, and we don't have any like terms on the left side or on the right side, so step one is all set, and we can move to step two, adding and subtracting to get variables on one side and constants on the other. We can see that our only constant is already on the left side, so let's keep constants on the left and move variables to the right. This means that we need to move this three x from the left, and we can get rid of it by subtracting three x from both sides of the equation. This is gonna cancel our three x on the left, leaving us with minus eight. And on the right, we get two x minus three x, which is minus x, or we can also think of it as minus one x. We're all set with step two, and now we can move on to step three using multiplication or division to isolate the variable. We wanna get rid of this minus one so we can divide both sides of the equation by minus one. And on the right, that's gonna cancel the minus one, just leaving us with x. And on the left, we get negative eight divided by negative one, which is just eight. So we end up getting that eight is equal to x. And that is step three all set. I encourage you to do step four and plug eight in for x back to the original equation to check your work. But once that's all set, you've solved the equation. Awesome job.

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Intermediate Algebra

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Solving Linear Equations

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객관식

Solve the following equations with fractions.
$\frac{x}{4} - \frac{2}{3} = \frac{x}{6}$

$x=$\frac$85$

$x=-8$

$x=8$

$x=-$\frac$85$

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검증된 단계별 안내

Start with the given equation: $\frac{x}{4} - \frac{2}{3} = \frac{x}{6}$.

To eliminate the fractions, find the least common denominator (LCD) of 4, 3, and 6, which is 12. Multiply every term in the equation by 12 to clear the denominators.

After multiplying, rewrite the equation without fractions: $12 \times \frac{x}{4} - 12 \times \frac{2}{3} = 12 \times \frac{x}{6}$, which simplifies to $3x - 8 = 2x$.

Isolate the variable $x$ by subtracting \$2x$ from both sides: \(3x - 2x - 8 = 0$, which simplifies to \)x - 8 = 0$.

Finally, solve for $x$ by adding 8 to both sides: $x = 8$.