Question

A carpenter cuts boards for a construction project. Each board must be 3 meters long, but the length is allowed to differ from this value by at most 0.5 centimeters. Write and solve an absolute-value equation to find the minimum and maximum acceptable lengths for a board.

A) 2.5 m and 3.5 m
B) 2.7 m and 3.3 m
C) 2.8 m and 3.2 m
D) 2.9 m and 3.1 m

Answer 1

To find the minimum and maximum acceptable lengths for a board, set up an absolute value equation and solve for x. The minimum acceptable length is 2.995 meters and the maximum acceptable length is 3.005 meters.

Step-by-step explanation:

To find the minimum and maximum acceptable lengths for a board, we can set up an absolute value equation. Let x be the length of the board. According to the problem, the length of the board can differ from 3 meters by at most 0.5 centimeters. This means that the length of the board can be either less than 3 meters or greater than 3 meters, but the difference cannot exceed 0.5 centimeters. Therefore, the absolute value equation is |x - 3| ≤ 0.005. To solve this equation, we have two cases:

Case 1: x - 3 ≤ 0.005

Solving for x, we have x ≤ 3.005

Case 2: -(x - 3) ≤ 0.005

Solving for x, we have -x + 3 ≤ 0.005

Adding x and subtracting 0.005 from both sides, we get x ≥ 2.995

Combining the two cases, the minimum acceptable length for a board is 2.995 meters (or 299.5 centimeters) and the maximum acceptable length is 3.005 meters (or 300.5 centimeters).