Answer:
x = 10
Explanation:
You want the value of x that satisfies x -(x-1)/3 -(2x-5)/5 +(x+8)/6 = 7.
Solution
The least common denominator is 5·6 = 30, so we can eliminate the fractions by multiplying by 30:
30x -10(x -1) -6(2x -5) +5(x +8) = 7·30
30x -10x +10 -12x +30 +5x +40 = 210 . . . . . eliminate parentheses
13x +80 = 210 . . . . . . . . . collect terms
13x = 130 . . . . . . . . . . subtract 80
x = 10 . . . . . . . . . . divide by 13
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Additional comment
Often an equation can be nicely solved by a graphing calculator. We like to write the equation in the form f(x) = 0, and look for the x-intercepts. Those are usually labeled by the calculator. Here that rewrite is accomplished by subtracting 7 from both sides.