Final answer:
The value of x that makes the linear equation 4(x - 2) - 6x = -2(2x + 4) + 8 true is 4.
Step-by-step explanation:
The question asks for the value of x that makes the given linear equation true: 4(x - 2) - 6x = -2(2x + 4) + 8. To find this value, we need to simplify and solve the equation for x. First, distribute and combine like terms on both sides:
4x - 8 - 6x = -4x - 8 + 8,
-2x - 8 = -4x,
Now, add 4x to both sides:
-2x + 4x - 8 = 0,
2x - 8 = 0.
Next, add 8 to both sides to isolate the x term:
2x = 8.
Finally, divide by 2 to solve for x:
x = 4.
So, the value of x that makes the equation true is 4.