Final answer:
To solve the equation 0.75(x+1)+1 = (x-2)+5, we distribute and combine like terms, then isolate x to find that x = 5, which is not included in the provided options.
Step-by-step explanation:
Step-by-step algebraic solution
To solve the algebraic equation 0.75(x+1)+1 = (x-2)+5, first we'll simplify both sides of the equation.
On the left side of the equation, distribute 0.75 to both x and 1:
0.75x + 0.75 + 1 = x - 2 + 5.
Combining like terms gives us:
0.75x + 1.75 = x + 3.
Then transfer the terms involving x on one side and the constants on the other:
0.75x - x = 3 - 1.75.
Simplifying further, we get:
-0.25x = 1.25.
Divide both sides by -0.25 to solve for x:
x = −1.25 / −0.25
This simplifies to:
x = 5
Therefore, none of the provided options a) x=12 b) x=8 c) x=6 d) x=4 are correct, as the solution for x is actually 5.