149. Решите уравнение:

Решение:

а) \(3x - 8 = x + 6\)

\(3x - x = 6 + 8\)

\(2x = 14\)

\(x = 7\)

б) \(7a - 10 = 2 - 4a\)

\(7a + 4a = 2 + 10\)

\(11a = 12\)

\(a = \frac{12}{11}\)

в) \(\frac{1}{6}y - \frac{1}{2} = 3 - \frac{1}{2}y\)

\(\frac{1}{6}y + \frac{1}{2}y = 3 + \frac{1}{2}\)

\(\frac{1}{6}y + \frac{3}{6}y = \frac{6}{2} + \frac{1}{2}\)

\(\frac{4}{6}y = \frac{7}{2}\)

\(\frac{2}{3}y = \frac{7}{2}\)

\(y = \frac{7}{2} \cdot \frac{3}{2}\)

\(y = \frac{21}{4}\)

\(y = 5.25\)

г) \(2,6 - 0,2b = 4,1 - 0,5b\)

\(-0,2b + 0,5b = 4,1 - 2,6\)

\(0,3b = 1,5\)

\(b = \frac{1,5}{0,3}\)

\(b = 5\)

д) \(p - \frac{1}{4} = \frac{3}{8} + \frac{1}{2}p\)

\(p - \frac{1}{2}p = \frac{3}{8} + \frac{1}{4}\)

\(\frac{1}{2}p = \frac{3}{8} + \frac{2}{8}\)

\(\frac{1}{2}p = \frac{5}{8}\)

\(p = \frac{5}{8} \cdot 2\)

\(p = \frac{5}{4}\)

\(p = 1.25\)

е) \(0,8 - y = 3,2 + y\)

\(0,8 - 3,2 = y + y\)

\(-2,4 = 2y\)

\(y = \frac{-2,4}{2}\)

\(y = -1,2\)

ж) \(\frac{2}{7}x = \frac{1}{2}\)

\(x = \frac{1}{2} \cdot \frac{7}{2}\)

\(x = \frac{7}{4}\)

\(x = 1.75\)

3) \(2x - 0,7x = 0\)

\(1,3x = 0\)

\(x = 0\)

Ответ: а) 7; б) 12/11; в) 5.25; г) 5; д) 1.25; е) -1.2; ж) 1.75; з) 0.