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.3(2x-5)-2(4x+1)=-5(x+3)-2

Accepted Answer

Hello, today we're going to be solving the given equation for X. So what we are given is four times the quantity two X minus three minus eight times the quantity five X plus two is equal to negative 16 times the quantity three X plus one minus 12. Now, in order to simplify this equation, the first thing we're gonna want to do is open up the parentheses. In order to do that, we're going to distribute four into two X minus three. We're going to distribute negative eight into five X plus two and we're going to distribute negative 16 into three X plus one that is going to give us eight X minus 12 minus 40 X minus 16 is equal to negative 48 X minus 16 minus 12. Now, on the left hand side, we're gonna go ahead and combine like terms, we can combine positive eight X and negative 40 X to give us negative 32 X and we can combine negative and negative 16 to give us negative 28. And on the right hand side of the equation, we can go ahead and combine negative 16 and negative 12 to give us negative 28. So we have negative 48 X minus 28. Now, in order to solve for X, we're going to want to move all of the X terms to the left hand side of the equation and move all the constants to the right hand side of the equation. That means we're going to add 48 X to both sides of the equation and we're going to add 28 to both sides. Now notice that if we add 28 to both sides of the equation, that's just going to cancel out the constants. And that is going to leave us with 16 X is equal to zero. And in order to solve for X, we're going to divide both sides by 16 and that is going to leave us with X is equal to zero, which is going to be the solution to the given equation. And with that being said, the answer to this problem is going to be B 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.3(2x-5)-2(4x+1)=-5(x+3)-2

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