SOLUTION: You are cutting boards as part of your training at a lumber yard. The length of a board must be 25 inches with an absolute deviation of at most 0.5 inch. Write an inequality t

Question 1010705: You are cutting boards as part of your training at a lumber yard. The length of a board must be 25 inches with an absolute deviation of at most 0.5 inch.
Write an inequality to find the possible lengths (in inches) of each board.

B.) What are the possible lengths of the boards you can cut?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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