Linear equations: 3(x - 6) + 2x = 67; 2x - (x + 15) = 63
- Thread starter JayCee
- Start date
Re: Linear equations
I'll help you through the first one:
3(x - 6) + 2x = 67
Multiply each term INSIDE the parentheses by the 3 which is outside:
3*x - 3*6 + 2x = 67
3x - 18 + 2x = 67
Simplify the expression to the left of the equals sign by combining like terms. 3x + 2x is 5x, so,
5x - 18 = 67
Now, add 18 to both sides. This will eliminate the "-18" from the left side, and leave just the variable term there:
5x - 18 + 18 = 67 + 18
Combine like terms again:
5x = 85
Finally, to get just "x" on the left side, divide both sides of the equation by 5:
(5x) / 5 = 85 / 5
x = 17
So, the original equation should be true if x = 17. Check. The original equation was
3(x - 6) + 2x = 67
Substitute 19 for x:
3(17 - 6) + 2(17) = 67
3(11) + 2(17) = 67
33 + 34 = 67
67 = 67
It checks.
Ok...you try the same method on the second equation.
If you have difficulty, please repost, showing all steps you've taken to solve the problem.
[/tex]
JayCee said:
I'll help you through the first one:
3(x - 6) + 2x = 67
Multiply each term INSIDE the parentheses by the 3 which is outside:
3*x - 3*6 + 2x = 67
3x - 18 + 2x = 67
Simplify the expression to the left of the equals sign by combining like terms. 3x + 2x is 5x, so,
5x - 18 = 67
Now, add 18 to both sides. This will eliminate the "-18" from the left side, and leave just the variable term there:
5x - 18 + 18 = 67 + 18
Combine like terms again:
5x = 85
Finally, to get just "x" on the left side, divide both sides of the equation by 5:
(5x) / 5 = 85 / 5
x = 17
So, the original equation should be true if x = 17. Check. The original equation was
3(x - 6) + 2x = 67
Substitute 19 for x:
3(17 - 6) + 2(17) = 67
3(11) + 2(17) = 67
33 + 34 = 67
67 = 67
It checks.
Ok...you try the same method on the second equation.
If you have difficulty, please repost, showing all steps you've taken to solve the problem.
[/tex]
Ok, I see what you did with the first equation which made it look so easy to me. I went and retried it with all the steps you did just to practice the first problem and it all made sense to me. However, the second problem is a little confusing to me because the subtraction sign at the beginning of it after the 2x through's me off. But I did make a attempt to it, and after doing the check it didn't add up correctly. If it was set up the same way as the first one I wouldn't have a problem with solving.
I greatly appreciate the work you put in to showing and helping me how to complete these. If you could help me out with the second one, at least for the beginning part I don't understand that would be very helpful. Thank you very much!
I greatly appreciate the work you put in to showing and helping me how to complete these. If you could help me out with the second one, at least for the beginning part I don't understand that would be very helpful. Thank you very much!
Alright I kept trying it out and figured out the answer, but it seems like I took different steps than the last one because that - sign at the beginning through me off. This is what I did:
2x-(x+15)=63
x+15=63
15x=63
-15 +15
x=78
check.
2*78-(78+15)=63
2x-(x+15)=63
x+15=63
15x=63
-15 +15
x=78
check.
2*78-(78+15)=63
Ok your right that makes more sense, even though I did it correctly and subtracted out the 2x to equal just x, that still gives me a better understanding, thanks. Now i've completed the problem by adding that into the beginning of it. Thanks again.skeeter said:
D
Deleted member 4993
Guest
JayCee said:
This is the correct way of figuring out the problem now. I've been busy with other studies and now decided to post up the correct way of determining the second problem.
2x-(x+15)=63
2x-x+15=63
2x-x=x
x-15= 63
-15+15=0
63+15=78
x=78
if theres any implications please let me know..thank you all!
2x-(x+15)=63
2x-x+15=63
2x-x=x
x-15= 63
-15+15=0
63+15=78
x=78
if theres any implications please let me know..thank you all!
D
Deleted member 4993
Guest
Although your "answer" is correct - the correct and "succinct" way to do this would be:
2x - (x+15) = 63
2x - x - 15 = 63
x - 15 = 63
x - 15 + 15 = 63 + 15
x = 78
2x - (x+15) = 63
2x - x - 15 = 63
x - 15 = 63
x - 15 + 15 = 63 + 15
x = 78