Solve the equation. Show all the steps for full credit.
5/2(6-8x)+3x=-83-3x
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To solve the equation 5/2(6-8x) + 3x = -83 - 3x, we begin by distributing the 5/2 to the terms inside the parentheses:
(5/2) * 6 - (5/2) * 8x + 3x = -83 - 3x
Now simplify both sides:
15 - 20x + 3x = -83 - 3x
Combine like terms on both sides of the equation:
-17x + 15 = -83 - 3x
Next, move all the x terms to one side by adding 17x to both sides:
-17x + 17x + 15 = -83 - 3x + 17x
The x terms cancel out on the left side:
15 = -83 + 14x
Now isolate the term with x by subtracting -83 from both sides:
15 + 83 = 14x
98 = 14x
To solve for x, divide both sides by 14:
98/14 = x
Simplifying the right side:
7 = x
Thus, the solution to the equation is x = 7.