Question

1)2x²-6x+4=0
2)x²+5x-14=0
3)3x-5<0

Answer 1

$1)2 {x}^{2} - 6x + 4 = 0 \: | \div 2$

${x}^{2} - 3x + 2 = 0$

${x}^{2} - x - 2x + 2 = 0$

$x(x - 1) - 2(x - 1) = 0$

$(x - 1)(x - 2) = 0$

$x - 1 = 0 = > x_{1} = 1$

$x - 2 = 0 = > x_{2} = 2$

$2) {x}^{2} + 5x - 14 = 0$

${x}^{2} + 7x - 2x - 14 = 0$

$x(x + 7) - 2(x + 7) = 0$

$(x + 7)(x - 2) = 0$

$x + 7 = 0 = > x_{1} = - 7$

$x - 2 = 0 = > x_{2} = 2$

$3)3x - 5 < 0$

$3x < 5$

$x < \frac{5}{3}$

$x \: \in \: ( - \infty , \frac{5}{3} )$