Solve each equation. 6(3x-1)= 8 - (10x-14)

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation. We have 12 times parentheses five x minus three. And parentheses equals 11 minus parentheses four X minus 17. And we are asked to solve this linear equation. Alright well when we look at this we see that we have two sets of parentheses inside the parentheses. They are not like terms, we can't take five x minus three and we can't take four x minus 17. However we can distribute what is squished up in front of these parentheses. So this 12 can be distributed to both the five X. And the negative three. And this invisible one here. This negative one can be distributed to the four X. And the negative 17 in this set of parentheses. So let's start off by doing that. We take 12 times five X. And that's going to equal 60 X. And 12 times negative three is going to be a minus 36 that equals spring down the 11. Now distributing the negative one to the forex, that's minus four X. And distributing the negative one to the negative 17 negative one, times negative 17 equals a positive 17. Now we can combine like terms on the right, we have this 11 plus 17 that we can do. So let's bring down the rest 60 X minus equals 11 plus 17 equals 28. And then bring down that minus four X. Now let's bring the X is to the same side. We can add four X to both sides to bring the X. Is to the left hand side. And then let's bring all of the constant terms to the same side. So we can add 36 to both sides. And so on the left, 60 x plus four x equals 64 x. Negative 36 plus 36 equals zero, which is what we wanted. So then equals 28 plus 36 equals 64 then negative four X plus four X equals zero, which is what we wanted. So now we have 64 X equals 64. To get that X by itself. We need to divide both sides by 64. And then on the left we have X by itself with X equals and 64 divided by 64 equals one. So all that and we get X equals one. We look at our answer choices in this matches with answer choice B. Well done. We'll catch you on the next one.

Solve each equation. 6(3x-1)= 8 - (10x-14)

Verified Solution

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations