Question

Evaluate the expression
|x+5|-|2w|Z=6

Answer 1

To evaluate the expression |x+5|-|2w|Z=6, substitute the given value of Z into the expression and solve for x and w. The solutions are (x=6, w=-2) and (x=-16, w=3).

Step-by-step explanation:

To evaluate the expression |x+5|-|2w|Z=6, we need to substitute the given value of Z into the expression and solve for x and w. Here are the steps:

1. Substitute Z=6 into the expression to get |x+5|-|2w|=6.
2. Solve the equation for two cases - when the expression inside the absolute value is positive and when it is negative.
3. Case 1: When x+5 is positive, we have x+5-|2w|=6. Simplify this equation to get x+2w=1.
4. Case 2: When x+5 is negative, we have -(x+5)-|2w|=6. Simplify this equation to get x+2w=-11.
5. Now we have two systems of equations: x+2w=1 and x+2w=-11. We can solve these systems simultaneously to find the values of x and w.

By solving the systems of equations, we find that x=6 and w=-2 for the case when x+5 is positive, and x=-16 and w=3 for the case when x+5 is negative. Therefore, the solutions to the original equation are (x=6, w=-2) and (x=-16, w=3).