Answer:
x= 2.5 and -3.5
Explanation:
To solve the equation Ix+1/2I=3, we can break it down into two cases: one where x+1/2 is positive, and one where x+1/2 is negative.
Case 1: x+1/2 is positive
In this case, the absolute value of x+1/2 is equal to x+1/2 itself. So we can rewrite the equation as x+1/2=3. To solve for x, we subtract 1/2 from both sides: x=3-1/2. Simplifying further, we have x=2.5.
Case 2: x+1/2 is negative
In this case, the absolute value of x+1/2 is equal to -(x+1/2). So we can rewrite the equation as -(x+1/2)=3. To solve for x, we first distribute the negative sign: -x-1/2=3. Then, we add 1/2 to both sides: -x=3+1/2. Simplifying further, we have -x=3.5. To isolate x, we multiply both sides by -1: x=-3.5.
So, the solution to the equation Ix+1/2I=3 is x=2.5 and x=-3.5.