SOLUTION: Solve the equation analytically. Check it analytically by direct substitution, and then support your solution graphically. 7/3(2x-1)=1/5x + 2/5(4-3x) I am really bad at this

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: Solve the equation analytically. Check it analytically by direct substitution, and then support your solution graphically. 7/3(2x-1)=1/5x + 2/5(4-3x) I am really bad at this      Log On

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Question 68960This question is from textbook
: Solve the equation analytically. Check it analytically by direct substitution, and then support your solution graphically.
7/3(2x-1)=1/5x + 2/5(4-3x)
I am really bad at this. Can you please explain it to me step-by-step. I know that you probably cannot graph it, but also can you somehow explain that part to me as well?This question is from textbook

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem you're given the task of finding which value of x will make that equation true. When you find your x value, plugging it back in (aka substitution) verifies your answer.
%287%2F3%29%2A%282x-1%29=%281%2F5%29%2Ax+%2B+%282%2F5%29%2A%284-3x%29So to start, distribute the fractions 7/3 and 2/5 among their respective terms
%2814%2F3%29x-7%2F3=%281%2F5%29x+%2B+%288%2F5-%286%2F5%29x%29 Simplify (1/5x-6/5x=-5/5x=-x)
%2814%2F3%29x-7%2F3=-x+%2B+8%2F5 Get similar terms to one side
%2814%2F3%29x%2Bx=8%2F5%2B7%2F3 get all terms with similar denominators
%2814%2F3%29x%2B%283%2F3%29x=24%2F15%2B35%2F15 Simplify
%2817%2F3%29x=59%2F15 Isolate x by multiplying by 3/17
cross%28%283%2F17%29%2A%2817%2F3%29%29x=%283%2F17%29%2A%2859%2F15%29Simplify
x=59%2F85
So at x=59/85 now we just need the y coordinate to finalize it. pick any side of the equality and plug in x=59/85 into the x variable. To save work, the y value is 77/85. At the point (59/85,77/85) the two lines intersect here since their x and y values are the same