Solve the equation. Show all the steps for full credit.
`\frac{5}{2}\left(6-8x\right)+3x=-83-3x`
Put your answer in the answer box below
(4 points)
To solve the equation, we will start by simplifying both sides.
On the left side, we use the distributive property to multiply `\frac{5}{2}` by both terms inside the parentheses:
`\frac{5}{2}(6-8x) = \frac{5}{2} \cdot 6 + \frac{5}{2} \cdot (-8x)`
`\frac{5}{2}(6-8x) = 15 - 20x`
On the right side, we combine the terms `-3x` and `3x`:
`-83 - 3x = -83 + (-3x) = -83 - 3x`
Now, the equation becomes:
`15 - 20x + 3x = -83 - 3x`
Next, we will combine like terms. On the left side, we add `-20x` and `3x`:
`15 - 20x + 3x = 15 - 17x`
On the right side, we add `-3x` to `-83`:
`-83 - 3x = -83 - 3x`
Now, the equation becomes:
`15 - 17x = -83 - 3x`
To solve for `x`, we need to isolate the variable `x`. We can do this by moving all terms with `x` to one side and all constant terms to the other side.
Starting with the equation:
`15 - 17x = -83 - 3x`
First, we add `17x` to both sides:
`15 - 17x + 17x = -83 - 3x + 17x`
Simplifying:
`15 = -83 + 14x`
Next, we add `83` to both sides:
`15 + 83 = -83 + 83 + 14x`
Simplifying:
`98 = 14x`
Finally, we divide both sides by `14` to isolate `x`:
`\frac{98}{14} = \frac{14x}{14}`
Simplifying:
`7 = x`
The solution to the equation is `x = 7`.