Solve: 3x-1/5 + x+2/2 = -3/10.

(Section 1.4, Example 4)

Question

Solve: 3x-1/5 + x+2/2 = -3/10.

(Section 1.4, Example 4)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve the following equation we have in the numerator, the difference of six X minus five that's divided by nine, that fraction plus in the numerator, we have the sum of X plus eight and that's all divided by four. And that is equal to, on the right hand side of the equation, we have negative 1/12. Our answer choices are answer choice A X equals negative five thirds. Answer choice B X equals negative 22 9th. Answer choice C X equals negative 1 12 and answer choice D no solution. All right, when we are solving for X and we've got fractions and an equal sign, we want to start off by getting rid of the fractions. And we do that by multiplying everything by the least common multiple of our denominators. So we want to ask ourselves, what is the lowest number that 94 and 12 all multiply into? And that is going to be a positive 36. So we want to multiply everything by a positive 36. And now we are going to reduce that 36 by whatever is in the denominator of each fraction that we're multiplying it by. So for the first one, we're multiplying 36 by a fraction with a denominator of nine and 36 divided by nine is a positive four. So really what we have is four multiplied by that numerator, which is the difference of six X minus five. And now we will reduce the 36 for the second fraction, 36 divided by four is a positive nine. So this is plus nine multiplied by the sum of X plus eight. And that's equal to. Now, we can reduce the fraction on the right hand side of the equal sign divided by 12 is a positive three and three multiplied by negative one is negative three. Now we can distribute the numbers in front of our parentheses. So we can distribute the four to the six X and the negative five and we can distribute the nine to the X and the multiplied by six. X is 24 X four multiplied by negative five is negative 20 nine, multiplied by X is a positive nine X and nine multiplied by eight is a positive 72. That all is still equal to negative three. Now, we want to bring our X terms together and we want to bring our constant terms together. So taking 24 X plus nine X, that's going to equal a positive 33 X and taking negative 20 plus 72 that's going to be a positive 52 that's still equal to negative three. Now, we want the X by itself on one side of the equation and all of the numbers on the other side will start off by moving that positive 52 to the right hand side. And because it's positive, we can subtract it, we subtract 52 from both sides because on the left positive minus 52 is zero and all we'll have over there is X that's equal to, on the right hand side, negative three minus 52 is a negative 55. And now to solve for X, we just need to divide by that 33 that X is being multiplied by and 33 divided by 33 on the left. That's a one. We have one X which is just X which is what we're looking for ya. And then on the right, we have a negative 55 divided by 33. Well, we can take that negative 33rd and we can simplify it. Both the numerator and the denominator are divisible by 11. Negative 55 divided by 11 is a negative five in the numerator and 33 divided by 11 is a positive three in the denominator. So X is equal to negative five thirds. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Solve: 3x-1/5 + x+2/2 = -3/10. (Section 1.4, Example 4)

Key Concepts

Linear Equations

Fraction Operations

Isolating the Variable

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