Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x ...

Question

Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

Accepted Answer

Welcome back. I'm so glad you're here. We've got this equation here, we've got seven times X minus one plus six equals three X minus seven minus X. And we're not only going to solve for X here but we are also going to take what we find and we're going to evaluate X squared plus two X. So let's start off by finding X. We're going to start off we're going to take this seven and distribute it to what's inside the parentheses. And we're going to take this negative invisible one here and distribute it to what's inside these parentheses so that we can get rid of the parentheses. So on the left hand side seven times X is seven X. Seven times negative one is minus seven and bring down plus six equals on the right hand side three X is brought down and then negative one times seven is minus seven negative one times negative X is plus one X. Or just plus X. Great. We have no more parentheses and now we can do the fun finding combining like terms. So on the left hand side we've got a negative seven and a six that can be combined and on the right the three X plus and X which can be combined. So on the left seven X is brought down negative seven plus six is minus one equals three X plus X is for X. Bring down that minus seven. Now what we want to do is we want to get the X by itself on one side and all the regular numbers by themselves on the other side And I'm going to do that by subtracting four X from both sides bringing the four X to the left so that I've got a positive X. Number. And so now we've got seven x minus four X. Which is three X. Bring down the minus one equals four X minus four X zero. So just negative seven on the right now let's bring that one to the other side. It's negative. So I'll add it to both sides and on the left hand side three X by itself because negative one plus one is nothing and on the right hand side negative seven plus one is negative six. Now I want to get that X by itself and so I'm going to say what's happening between the three and the X. Well the three is being multiplied. What's the opposite of that division? I'm going to divide it by three. And what I do to one side I have to do to the other on the left hand side, three divided by three. That's just one. So now we've got one X. Or just X on the left and on the right, negative three divided or negative six divided by three is negative two. Well cool, now don't just click and start clicking B just yet because remember we have to go back in and substitute X equals negative two for this X squared plus two X. Expression. So it's no longer X squared. It's now negative two squared plus two times not X, but negative two negative two squared is four positive for and two times negative two is negative four. So four plus negative four. Well that's zero. So that gets us answer choice D. Well done. We'll catch on the next one.

Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

Key Concepts

Solving Linear Equations

Quadratic Expressions

Substitution

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