Question

é muito urgente !!!!

Sendo U = Q.

A) $\frac{5x}{4} - 1 > x - \frac{5}{8}$

b) $0.6 + \frac{y}{2} \geq \frac{5}{6} - y$

c) $\frac{7x}{6} - 0.25 < \frac{2x}{3}$

d) $\frac{2x-4}{9}< \frac{4x+1}{3}$

e) $\frac{1}{3} \geq 0.75 (8t- \frac{2}{9})$

f) $\frac{3}{5} (3x-2) < \frac{2}{3} (2x+1)$

Preciso de calculos !!!!!!!! 

Answer 1

Oi Jennifer. Aí estão os cálculos.
$a) \frac{5x}{4} -1>x- \frac{5}{8} \\ \\ \frac{10x-8>8x-5}{8} =10x-8x>-5+8 \\ \\ 2x>3 \\ \\ x>3/2$

$b) 0.6+ \frac{y}{2} \geq \frac{5}{6}-y \\ \\ \frac{6}{10}+ \frac{y}{2} \geq \frac{5}{6}-y \\ \\ \frac{18+15y \geq 25-30y}{30} =18+15y \geq 25-30y \\ \\ 15y+30y \geq 25-18 \\ \\ 45y \geq 7 \\ y \geq 7/45$

$c) \frac{7x}{6} -0.25< \frac{2x}{3} \\ \\ \frac{7x}{6} - \frac{25}{100} < \frac{2x}{3} \\ \\ \frac{350x-75<200x}{300}= 350x-75<200x \\ \\ 350x-200x<75 \\ 150x<75 \\ x<75/150 \\ x<0.5$

$d) \frac{1}{3} \geq 0.75(8t- \frac{2}{9} ) \\ \\ \frac{1}{3} \geq \frac{75}{100} (8t- \frac{2}{9} ) \\ \\ \frac{1}{3} \geq \frac{600t}{100}- \frac{150}{900} \\ \\ \frac{1}{3} \geq 6t- \frac{1}{6} \\ \\ \frac{2 \geq 36t-1}{6} =2 \geq 36t-1 \\ \\ -36t \geq -1-2 \\ \\ -36t \geq -3 \ \ \ \ *(-1) \\ \\ 36t \leq 3 \\ \\ t \leq 3/36 \\ \\ t \leq 1/12$

$e) \frac{2x-4}{9} < \frac{4x+1}{3} \\ \\ \frac{2x-4<3(4x+1)}{9} = 2x-4<3(4x+1) \\ \\ 2x-4<12x+3 \\ \\ 2x-12x<3+4 \\ \\ -10x<7 \ \ \ \ *(-1) \\ \\ 10x>-7 \\ \\ x>-7/10$

$f) \frac{3}{5}(3x-2)< \frac{2}{3}(2x+1) \\ \\ \frac{9x}{5}- \frac{6}{5} < \frac{4x}{3}+ \frac{2}{3} \\ \\ \frac{27x-18<20x+10}{15} = 27x-18<20x+10 \\ \\ 27x-20x <10+18 \\ 7x<28 \\ x<28/7 \\ x<4$

Answer 2

$a)\\ \frac{5x}{4}-1>x-\frac{5}{8}\\ \\ 10x-8>8x-5\\ \\ 10x-8x>-5+8\\ \\ 2x>3\\ \\ x>\frac{3}{2}$

$b)\\ 0,6+\frac{y}{2} \geq \frac{5}{6}-y\\ \\ \frac{6}{10}+\frac{y}{2} \geq \frac{5}{6}-y\\ \\ 18+15y \geq 25-30y\\ \\ 15y+30y \geq 25-18\\ \\ 45y \geq 7\\ \\ y \geq \frac{7}{45}$

$c) \\ \frac{7x}{6}-0,25<\frac{2x}{3}\\ \\ \frac{7x}{6}-\frac{1}{4}<\frac{2x}{3}\\ \\ 14x-3<8x\\ \\ 14x-8x<3\\ \\ 6x<3\\ \\ x<\frac{1}{2}$

$d)\\ \frac{2x-4}{9}<\frac{4x+1}{3}\\ \\ 2x-4<12x+3\\ \\ 2x-12x<3+4\\ \\ -10x<7\\ \\ x>-\frac{7}{10}$

$e)\\ \frac{1}{3} \geq 0,75(8t-\frac{2}{9})\\ \\ \frac{1}{3} \geq \frac{3}{4}(8t-\frac{2}{9})\\ \\ 4 \geq 8t-\frac{2}{9}\\ \\ 36 \geq 72t-2\\ \\ 38 \geq 72t\\ \\ 72t \leq 38\\ \\ t \leq \frac{38}{72}=\frac{19}{36}$

$f)\\ \frac{3}{5}(3x-2)<\frac{2}{3}(2x+1)\\ \\ 9(3x-2)<10(2x+1)\\ \\ 27x-18<20x+10\\ \\ 27x-20x>10+18\\ \\ 7x>28\\ \\ x>4$