№6. Выполните приведение подобных слагаемых: a) 10a + b − 10b − a; б) −8y + 7x + 6y + 7x; в) −8x + 5,2a + 3x + 5a; г) 5a + 7a − 9,2m + 15m; д) \(\frac{2}{7}\)x − \(\frac{4}{9}\)y − \(\frac{5}{14}\)x + \(\frac{2}{3}\)y; e) −6a + 5a − x + 4; ж) 23x − 23 + 40 + 4x; з) −a + x + 1,1a − 1,3x; и) −12p + 3k + 3,2p − 2,3k; к) 0,5a − \(\frac{2}{3}\)b − \(\frac{2}{5}\)a − \(\frac{1}{3}\)b.

Решение:

№6.

1. \(10a + b − 10b − a = (10a - a) + (b - 10b) = 9a - 9b\)
2. \(-8y + 7x + 6y + 7x = (7x + 7x) + (-8y + 6y) = 14x - 2y\)
3. \(-8x + 5,2a + 3x + 5a = (5,2a + 5a) + (-8x + 3x) = 10,2a - 5x\)
4. \(5a + 7a − 9,2m + 15m = (5a + 7a) + (-9,2m + 15m) = 12a + 5,8m\)
5. \(\frac{2}{7}x − \frac{4}{9}y − \frac{5}{14}x + \frac{2}{3}y = (\frac{2}{7}x - \frac{5}{14}x) + (-\frac{4}{9}y + \frac{2}{3}y) = (\frac{4}{14}x - \frac{5}{14}x) + (-\frac{4}{9}y + \frac{6}{9}y) = -\frac{1}{14}x + \frac{2}{9}y\)
6. \(-6a + 5a − x + 4 = (-6a + 5a) - x + 4 = -a - x + 4\)
7. \(23x − 23 + 40 + 4x = (23x + 4x) + (-23 + 40) = 27x + 17\)
8. \(-a + x + 1,1a − 1,3x = (-a + 1,1a) + (x - 1,3x) = 0,1a - 0,3x\)
9. \(-12p + 3k + 3,2p − 2,3k = (-12p + 3,2p) + (3k - 2,3k) = -8,8p + 0,7k\)
10. \(0,5a − \frac{2}{3}b − \frac{2}{5}a − \frac{1}{3}b = (0,5a - \frac{2}{5}a) + (-\frac{2}{3}b - \frac{1}{3}b) = (\frac{1}{2}a - \frac{2}{5}a) + (-\frac{3}{3}b) = (\frac{5}{10}a - \frac{4}{10}a) - b = \frac{1}{10}a - b\)