Solve each equation.

Question

Solve each equation. $\frac{5}{6}x - 2x + \frac{4}{3} = \frac{5}{3}$

Accepted Answer

Welcome back. I am so glad you're here. We are Given this linear equation, we have seven X divided by 12 minus four X plus 5/6 equal to +76. And we're asked to solve this linear equation. Well we've got all these yucky looking fractions here. So what I'd like to do first is get rid of our fractions. In order to do that. We need to look and find the lowest common denominator. So we look at 12 6 and six. The lowest common denominator here is 12, meaning we're going to take each term and multiply it by 12 so that will look like this. We have 12 times seven X over 12 - times four x Plus 12 times 5/6 Equals 12 times 7/6. And now we can do some simplification for the first multiplication here. 12 times seven X over 12. Those 12 will cancel out those become ones and that's just seven X. For the next one we can't simplify at all. We just have negative 12 times four X. Which is going to be minus 48 X. For the third one here we have 12 times 5/6 the 12 and the six reduce each other. They're both divisible by six. So six divided by six is one and 12 divided by six is two. So we just have two times five which equals plus and then equals and now for this one is very similar to the 12 and the six are both both divisible by 66 divided by six is one and 12 divided by six is two. And so we take two times seven which equals 14. Now on the left hand side we want to combine like terms we have this seven x minus 48 x and seven x minus 48 X. Leaves us with a negative 41 X. Bring down the plus 10 equals 14. We want to get X by itself. So we want all the constant terms on the opposite side. So we can subtract 10 from both sides to bring all the constant terms to the right hand side of the equation. That leaves us with negative 41 X on the left, 10 minus 10. Those cancel out that zero as intended and negative 41 X equals 14 minus 10 which equals four X is almost by itself. It's being multiplied by that negative 41. So we want to divide it and both sides by negative 41. So on the left we have negative 41 divided by negative 41. That's one or one X is just X. So we have X equals on the left. Yay And on the right hand side it's four divided by negative 41. We can put the negative on top. So we can say this is X equals negative 4 firsts we look at our answer choices and that matches with answer choice. D Well done. We'll catch you on the next one

Solve each equation. $\frac{5}{6}\)x - 2x + \(\frac{4}{3}\) = \(\frac{5}{3}$

Key Concepts

Solving Linear Equations

Combining Like Terms

Working with Fractions in Equations

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