Final answer:
To solve the linear equation provided, distribute the multiplication over parentheses, combine like terms, and isolate x to find that the solution is x = -22.
Step-by-step explanation:
To solve for x, we will first distribute the multiplication over the subtraction in the parentheses and then simplify the equation by combining like terms and isolating the variable x. Here are the steps:
- Distribute the 5 to the terms inside the parentheses: 5(8) - 5(x) + 36 = 102 - 2(3x + 24).
- The equation becomes: 40 - 5x + 36 = 102 - 6x - 48.
- Combine like terms: 76 - 5x = 54 - 6x.
- Add 6x to both sides: 76 - 5x + 6x = 54 - 6x + 6x, which simplifies to 76 + x = 54.
- Subtract 76 from both sides: x = 54 - 76.
- Calculate the value of x: x = -22.
Thus, the solution to the equation is x = -22.