In Exercises 61–66, find all values of x satisfying the given con...

Question

In Exercises 61–66, find all values of x satisfying the given conditions.

y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

Accepted Answer

Welcome back. I'm so glad you're here. We've got three equations here. The first one is Y sub one equals six times three X plus one minus seven. The second one is Y sub two equals four times X minus four plus eight. And the third one is just that why? Sub one equals Y sub two. And this is great because our third equation here, Y sub one equals Y sub two. Well that is just showing inequality between the first two equations. So we can use substitution where we've got a Y sub one, we can substitute in six times three X plus one minus seven which is equal to Y sub two. And again we use substitution for Y sub two. We are going to write four times X minus four plus eight. Great. Now for our next step let's get rid of these parentheses. Let's distribute the numbers switched up in front of the parentheses to get rid of those. So six times three X is eight 18 X. Six times one is plus six. Bring down that minus +74 times X is four X times and then four times negative four is minus 16. Bring down that plus eight. Great. Now let's look for like terms on the left hand side, we've got a plus six and minus seven on the right hand side. We've got a minus 16 and a plus eight. We'll bring down our 18 x plus six minus seven is minus one. Bring down our four X. On the right hand side, negative 16 plus eight is minus eight. Great. Now let's work on getting the excess together and all the other numbers on the other side. I'm going to choose to bring over this four X. Because then I've got a positive X. Value. So subtracting four X. From both sides 18 x minus four X. Is 14 X. On the left. Bring down minus one equals negative eight. And now let's bring that Native 1 to the other side. I'm going to add one to both sides on the left hand side. Now it's just 14 X. Because negative one plus one is zero. And on the right hand side negative eight plus one is negative seven. Now that 14 is being multiplied by the X. So I'm going to undo that with division what we divide on one side we have to divide on the other on the left hand side 14 divided by 14. That's just one. So on the left hand side it is a one X. Or just an X. And on the right hand side negative seven divided by 14. Well that is negative one half. We look at our answer choices and that matches with answer choice a while done we'll catch you on the next one

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