Solve Linear Equation: -31+48x+46 = 83x-85+15x

To solve the given linear equation $-31 + 48x + 46 = 83x - 85 + 15x$, we'll follow these steps:

• Step 1: Simplify both sides by combining like terms.
• Step 2: Move all $x$-terms to one side and constant terms to the other.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Simplify both sides of the equation:
On the left side, combine like terms: $-31 + 46 = 15$. Thus, the left side becomes $15 + 48x$.
On the right side, combine the $x$-terms: $83x + 15x = 98x$. The right side becomes $98x - 85$.

The equation now reads: $15 + 48x = 98x - 85$.

Step 2: Move all $x$-terms to one side and constant terms to the other:
Subtract $48x$ from both sides: $15 = 98x - 48x - 85$.
Simplify the $x$-terms: $98x - 48x = 50x$. Thus, $15 = 50x - 85$.

Add 85 to both sides: $15 + 85 = 50x$, resulting in $100 = 50x$.

Step 3: Solve for $x$ by dividing both sides by 50:
$x = \frac{100}{50} = 2$.

Therefore, the solution to the problem is $x = 2$.