Final answer:
To find the value of x in the equation, expand and simplify both sides, combine like terms, and solve by isolation of the variable x. The final solution is x = 0.6984 when rounded to four decimal places.
Step-by-step explanation:
To solve for the value of x in the equation 32(4x – 1) – 3x = 54 –(x + 2), first, expand and simplify:
- Multiply 32 by each term inside the parentheses: 32*4x - 32*1 = 128x - 32.
- Distribute the negative sign on the right side of the equation: -x - 2.
- Combine like terms on both sides and move all terms involving x to one side: 128x - 3x + x = 54 + 2 + 32.
- Simplify: 126x = 88.
- Divide both sides by 126 to isolate x: x = 88 / 126.
After simplifying the fraction, the solution is x = 0.6984 (rounded to four decimal places).