Solve each equation. 4[2x-(3-x)+5] = -6x - 28

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation. We have six times bracket seven x minus parentheses five minus two X. And parentheses plus 11. And bracket equals negative 11 x minus 29. Quite a bit going on here. We need to solve the linear equation so we need to get X by itself on one side. But there's a lot of operations going on here. So we recall from previous lessons the order of operations, parentheses, exponents, multiplication and division from left to right and then addition and subtraction from left, right or pem does. And so we start off looking for parentheses. We want the innermost parentheses. Well that's here with this five minus two X. However we can't do what's inside the parentheses because five and negative two X. Are not like terms we can't combine those. So what that means is we look and see if we can get rid of the parentheses and we can we've got this negative invisible one here squished up in front of the parentheses. That needs to be distributed to the two terms inside of the parentheses. So let's start off by doing that negative one times five is negative five and negative one times negative two X. Is positive two X. There we go. The parentheses. Now we can bring down the rest inside of the brackets is still the seven X. And then the minus five plus two X and plus 11. And that's all still being multiplied by the six and it's all still equal to negative 11 X minus 29. So now kind of starting from scratch again looking at the parentheses, seeing if we can do anything inside of those And here we can we can take our seven X plus the two X. That equals nine X. And we can take our negative five plus 11. That equals a positive six. That's all still inside the brackets. Still being multiplied by six, still equal to negative 11 X minus 29. And next we say okay we can't combine nine X. And six. They aren't like terms. So we need to distribute this six in front of the brackets so we'll take six times nine X. And six times 66 times nine X. Is 54 X. And six times six is a positive 36. That's all still equal to negative 11 X minus 29. Alright, we're getting close now we want to get our exes all together on one side of the equation and get our constant terms together on the other side. And so I'm going to add 11 X to both sides so that our exes will be positive on the left hand side. And I'm going to subtract 36 from both sides. So that are constant terms will be together on the opposite side of where the Xs are. So on the left hand side, 54 X plus 11 X equals 65 X. 36 minus 36 equals zero as we had intended. This 65 X. Is equal to negative 11 X plus 11 X. That's zero as we'd intended. And negative 29 minus 36 equals negative 65. We are so close X is almost by itself. That's being multiplied by that 65. So we just need to divide it and divide both sides by 65. So on the left 65 divided by 65. That's just one. So we have one X. Or just X equals negative 65 divided by 65. Well that simplifies to a negative one. So all that for X equals negative one. We look at our answer choices and this matches with answer choice. B. Well done. We'll catch you on the next one.

Solve each equation. 4[2x-(3-x)+5] = -6x - 28

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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