Solve each equation. 3x+5 - 5(x+1)= 6x+7

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation. We have six X plus seven minus four times parentheses. X plus four end parentheses. And that's equal to five X plus nine. And we are to solve this linear equation or to get X by itself. Well in order to do that, we first see that we've got this set of parentheses here. We can't combine the two terms inside of the parentheses. We can't take X plus four. So to get rid of those parentheses, we need to distribute what's in for one of them. So we need to take this negative four times the X. And times the positive four. So let's do that negative four times X. Is negative four X. And negative four times positive four is negative 16. Now we can bring down the rest. This still has the six X plus seven and this is all still equal to five X plus nine. Now there's no parentheses and we just go to addition and subtraction. And we want to add and subtract like terms on the left. We have a six x minus four X six X minus four X. Leaves us with two Xs. And we also have this seven minus 16, 7 minus 16 equals a negative nine and that equals five X plus nine. Still all right. And next we've got all of the addition and subtraction done on the left and right. That we can do these are not like terms on the same side. So we want to bring the like terms together. We want the excess all together on one side and the constant terms together on the other side. So I'm going to subtract two X from both sides so that our exes will be positive on the right hand side and then I'm going to subtract nine from both sides. So that are constant terms will be together on the side. That's opposite of where the Xs are. So on the left two x minus two X is zero as intended, negative nine minus nine equals a negative 18. And that is equal to five X minus two X which equals three X. And positive nine minus nine. That's zero as we'd intended X is almost by itself. It's being multiplied by that three. In order to get rid of that three. We need to divide by three and what we do to one side we need to do to the other as well. So on the left, negative 18 divided by three equals and negative six and that equals on the right, three divided by three is 11. X. Is just X. So we have X equals negative six. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one

Solve each equation. 3x+5 - 5(x+1)= 6x+7

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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