The length of the segment AB = 6 cm. The point M is taken inside the segment. Find the length of the segment BM if 2BM + 3AM = 14.

univerkov | December 1, 2020 | education

Let BM = x, then AM = AB – BM = 6 – x
1) 6 – x = 2x; 3x = 6; x = 2
2) 2 * (6 – x) = 3x; 12 – 2x = 3x; 5x = 12; x = 2.4
3) (6 – x) / x = 1/5; x = 5 * (6 – x); x = 30 – 5x; 6x = 30; x = 5
4) (6 – x) / x = 3/4; 3x = 4 * (6 – x); 3x = 24 – 4x; 7x = 24; x = 24/7
5) 6 – x – x = 2; 2x = 4; x = 2
6) 2x + 3 * (6 – x) = 14; 2x + 18 – 3x = 14; 3x = 4; x = 4/3

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