Question 1010705
absolute deviation equals the absolute value of the deviation from the desired measurement.


the desired measurement = 25 inches.


the absolute deviation would be .5 inches.


the board can measure between 24.5 and 25.5 and would be within the desired limits.


the absolute value inequality for this would be |25-x| <= .5 or |x-25| <= .5


assuming |25-x| <= 5, you get 2 equations.


if 25-x > 0, the equation becomes 25-x <= .5 which results in 24.5 <= x.


if 25-x < 0, the equation becomes 25-x >= -.5 which results in 25.5 >= x which is the same as x <= 25.5.


combining these two results yields 24.5 <= x <= 25.5 which represent the possible length that each board can be.


assuming |x-25| <= .5, you get 2 equations.


if x-25 > 0, the equation becomes x-25 <= .5 which results in x <= 25.5


if x-25 < 0, the equation becomes x-25 >= -.5 which results in x >= 24.5 which is the same as 24.5 <= x


combine the two results together and you get 24.5 <= x <= 25.5 which is the same result as the previous equation.


in other words, the equations |25-x| < .5 and |x-25| <= .5 are equivalent.