Question

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)

Answer 1

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`.