In Exercises 1–14, simplify the expression or solve the equation,...

Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate.4x-2(1-x)=3(2x+1)-5

Accepted Answer

Hello, today we're gonna be solving the equation for X. So what we are given is seven X minus three times the quantity five minus X is equal to two times five X plus three minus 21. Now, in order to sell for X, the first thing we're gonna want to do is to open up the parentheses. And in order to do that, we're going to distribute negative three into five Binance X and we're going to distribute two into five X plus three. That is going to give us seven X minus 15 plus three. X is equal to 10 X plus six minus 21. Now, on the left hand side, we're gonna go ahead and combine the light terms seven X and three X can be combined together to give us 10 X. So on the left hand side, we have 10 X minus 15. And on the right hand side, we can go ahead and combine negative 21 positive six together to give us X minus 15. Now, in order to further simplify, we can go ahead and add 15 to both sides of the equation to give us 10 X is equal to 10 X. And notice that if we divide both sides by 10, that is going to leave us with X is equal to X. So that means that any number of X that we plug into the equation is just going to equal to itself. Or in other words, there are infinitely many solutions to this given equation. And so we can go ahead and represent that as a set of numbers. What this means is that X is the set of numbers such that X can be any real number. And with that being said, this is going to be the solution to the given equation. And that means the answer to this problem is going to be C So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate.4x-2(1-x)=3(2x+1)-5

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