1. **State the problem:** We need to find the value of the expression $$v + w + x + y + z = 8$$ given the values of the variables. 2. **Given values:** - $$v = 3$$ - $$w = -2$$ - $$z = 4$$ (first mention) - $$y = -5$$ - $$z = 8$$ (second mention, likely a typo, we will use the second value as it appears last) 3. **Clarify variable values:** Since $$z$$ is given twice, we take the last value $$z = 8$$. 4. **Substitute known values into the equation:** $$3 + (-2) + x + (-5) + 8 = 8$$ 5. **Simplify the known terms:** $$3 - 2 - 5 + 8 + x = 8$$ $$ (3 - 2) = 1$$ $$1 - 5 = -4$$ $$-4 + 8 = 4$$ So the equation becomes: $$4 + x = 8$$ 6. **Solve for $$x$$:** $$x = 8 - 4$$ $$x = 4$$ 7. **Final answer:** $$x = 4$$ This means the value of $$x$$ that satisfies the equation with the given values is $$4$$.