Question

atividade de Matemática:
a)16x+>10x-8
b)9x-4<6x+8
c)2x(x-9)>22
​

Answer 1

Resposta:

a)

$16x > 10x - 8 \\ \\ 16x - 10x > - 8 \\ \\ 6x > - 8 \\ \\ x > - \dfrac{8 \div 2}{6 \div 2} \\ \\ \Large \boxed{ \green{ x > \bf - \dfrac{4}{3} }}$

b)

$9x - 4 < 6x + 8 \\ \\ 9x - 6x < 8 + 4 \\ \\ 3x < 12 \\ \\ x < \dfrac{12}{3} \\ \\ \Large \boxed{ \green{ x < \bf \: 4}}$

c)

$2x(x - 9) > 22 \\ \\ 2 {x}^{2} - 18x > 22 \\ \\ 2 {x}^{2} - 18x - 22 > 0 \\ \\ \delta = {b}^{2} - 4ac \\ \\ \delta = ( - 18) {}^{2} - 4(2)( - 22) \\ \\ \delta = 324 + 176 \\ \\ \delta = 500 \\ \\ Bhaskára \: \\ \frac{ - b \pm \: \sqrt{ \delta} }{2a} \\ \\ \frac{ - ( - 18) \pm \sqrt{500} }{2(2)} \\ \\ \frac{18 \pm \: \sqrt{500} }{4} \\ \\ \frac{18 \pm \sqrt{100 \times 5} }{4} \\ \\ \frac{18 \pm \sqrt{100} \times \sqrt{5} }{4} \\ \\ \frac{18 \pm \: 10 \sqrt{5} }{4 } \\ \\ { x1 = \frac{18 \div 2 + 10 \sqrt{5} \div 2}{4 \div 2} }\\ \\\Large \boxed{ \green{x1 = \bf \frac{9 + 5 \sqrt{5} }{2} } }\\ \\ x2 = \frac{18 \div 2 - 10 \sqrt{5 } \div 2}{4 \div 2} \\ \\ \Large\boxed{ \green{x2 = \bf \frac{9 - 5 \sqrt{5} }{2} }}$

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