Question

Rezolvați ecuațiile și inecuația: a)3x = 120 - x
b) 12x — 61 = 9
c)x² – 9x + 8 = 0
d)2x – 1> 4x – 8​

Answer 1

Răspuns:

$a)3x = 120 - x \\ 3x + x = 120 \\ 4x = 120 \\ 4x \div 4 = 120 \div 4 \\ x = 30$

$b)12x - 61 = 9 \\ 12x = 9 + 61 \\ 12x \div 12 = 70 \div 12 \\ x = \frac{70}{12} \\ x = \frac{35}{6} = 5 \times \frac{5}{6}$

$c) {x}^{2} - 9x + 8 = 0 \\ {x}^{2} - x - 8x + 8 = 0 \\ x - (x - 1) - 8(x - 1) = 0 \\ (x - 1)(x - 8) = 0 \\ x - 1 = 0 \\ x - 8 = 0 \\ x = 1 \\ x = 8$

$d)2x - 1 > 4x - 8 \\ 2x - 4x > - 8 + 1 \\ - 2x \div ( - 2) > - 7 \div ( - 2) \\ x < - 7 \div ( - 2) \\ x < \frac{7}{2} \\ x < 3 \times \frac{1}{2} \\ si \: x \: apartine \: de \: la \: - \infty \: pana \: la \: \frac{7}{2}$