Solve: 9(x − 1) = 1 + 3(x−2).
(Section 1.4, Example 3)

Question

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve the following equation. We're given seven multiplied by the difference of X minus six is equal to two plus four, multiplied by the difference of X minus five. Our answer choices are answer choice A X equals eight, answer choice B X equals 12. Answer choice C X equals 14 and answer choice D X equals 18. All right to solve for X, we want to get X all by itself on one side of the equal sign. We've got an X on both sides. So we want to bring those XS together right now. The XS are trapped inside of parentheses. So we need to free them. We'll need to free them by distributing the numbers in front of the parentheses. So distributing the seven to the X and the negative six and distributing the four to its X and the negative five. So let's do that. We have seven multiplied by X which is seven X and seven multiplied by negative six, which is a negative 42. That's all equal to still two plus, then four multiplied by X is four, X and four multiplied by negative five is a negative 20. We have freed the XS from their parentheses. Now, we just need to bring them together on the same side of the equal sign. So I like to when possible keep the number in front of the X positive. So I'm going to bring the four X over to the left because that four X is being added, we are going to subtract it and what we do to one side, we need to do to the other as well. And on the right where we have a four X minus four X, that will be zero. Now, we also want to bring all of the constant terms to the opposite side of the equal sign from where the X is. And so we want to bring this negative 42 over to the right hand side. So because it's being subtracted, we want to add it, we're adding 42 to both sides of the equal sign because on the left negative 42 plus 42 will be zero. Now, let's simplify, we have seven X minus four X that will be a positive three X that's equal to on the right, we have two minus 20 which is a negative 18 and then plus the 42 negative 18 plus 42 is a positive 24. Now we have three X equals 24. The three is being multiplied by the X and to get that over to the other side, we need to do the opposite operation which is division. So we will divide by three. What we do to one side we do to the other as well. On the left three X divided by three, the three divided by three is one. So we have one X which is just X, which is exactly what we wanted. X is by itself. Yay. On the right 24 divided by three is a positive eight. And we have solved for X X is equal to eight. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Solve: 9(x − 1) = 1 + 3(x−2). (Section 1.4, Example 3)

Key Concepts

Distributive Property

Combining Like Terms

Isolating the Variable

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