Question

за 1 пример
Решить Неравенство ​

Answer 1

$\frac{5}{6}(7+9y)\leq 14\frac{2}{3}-\frac{7}{8}(5y-8)\\\\\frac{5}{6}(7+9y)\leq\frac{44}{3}-\frac{7}{8}(5y-8)\\ \\\frac{5}{6}*7+\frac{5}{6}*9y\leq\frac{44}{3}-\frac{7}{8}*5y-\frac{7}{8}*(-8)\\\\\frac{35}{6}+\frac{45y}{6}\leq \frac{44}{3}-\frac{35y}{8} +\frac{56}{8}\\\\\frac{45y}{6}+\frac{35y}{8}\leq \frac{44}{3}+\frac{56}{8}-\frac{35}{6} \\\\\frac{180y}{24}+\frac{105y}{24}\leq\frac{352}{24}+\frac{168}{24}-\frac{140}{24}\\$

$\frac{285y}{24}\leq\frac{520}{24}-\frac{140}{2}\\\\\frac{285}{24}y\leq\frac{380}{24}\\\\y\leq \frac{380}{24}:\frac{285}{24}\\\\y\leq \frac{380}{24}*\frac{24}{285}\\\\y\leq \frac{76}{1} *\frac{1}{57}\\\\y\leq \frac{76}{57}\\\\y\leq1 \frac{19}{57}\\\\y\leq 1\frac{1}{3}$

y ∈ ( -∞ ; $1\frac{1}{3}$ ]

Answer 2

6

5

(7+9y)≤14

3

2

−

8

7

(5y−8)

6

5

(7+9y)≤

3

44

−

8

7

(5y−8)

6

5

∗7+

6

5

∗9y≤

3

44

−

8

7

∗5y−

8

7

∗(−8)

6

35

+

6

45y

≤

3

44

−

8

35y

+

8

56

6

45y

+

8

35y

≤

3

44

+

8

56

−

6

35

24

180y

+

24

105y

≤

24

352

+

24

168

−

24

140

\begin{gathered}\frac{285y}{24}\leq\frac{520}{24}-\frac{140}{2}frac{285}{24}y\leq\frac{380}{24}y\leq \frac{380}{24}:\frac{285}{24}y\leq \frac{380}{24}*\frac{24}{285}y\leq \frac{76}{1} *\frac{1}{57}y\leq \frac{76}{57}y\leq1 \frac{19}{57}y\leq 1\frac{1}{3}\end{gathered}

24

285y

≤

24

520

−

2

140

24

285

y≤

24

380

y≤

24

380

:

24

285

y≤

24

380

∗

285

24

y≤

1

76

∗

57

1

y≤

57

76

y≤1

57

19

y≤1

3

1

y ∈ ( -∞ ; 1\frac{1}{3}1

3

1

]