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`.
Solve the equation. Show all the steps for full credit.
`\frac{5}{2}\left(6-8x\right)+3x=-83-3x`
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(4 points)
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