Question

5/6(7+9y)=<7 1/2-7/8(5y-8)​

Answer 1

Ответ:

y≤16/285

Пошаговое объяснение:

5/6(7+9y)≤7 1/2-7/8(5y-8)​

35/6+15y/2≤15/2-35y/8-7

15y/2+35y/8≤15/2-7-35/6

60y/8+35y/8≤91/14-35/6

95y/8≤273/42-245/42

95y/8≤28/42

95y≤28/42×8

95y≤112/21

y≤112/21÷95

y≤112/21×1/95

y≤112/1995

y≤16/285

Answer 2

To solve the equation 5/6(7+9y) <= 7 1/2 - 7/8(5y-8), we need to simplify and isolate the variable y. Let's break down the steps:

Step 1: Distribute and simplify the equation on both sides:

On the left side: 5/6(7+9y) = (5/6) * 7 + (5/6) * 9y = 35/6 + 15/2y = (35 + 45y)/6

On the right side: 7 1/2 - 7/8(5y-8) = 15/2 - (7/8) * (5y-8) = 15/2 - (35y/8 - 7/8 * 8) = 15/2 - (35y/8 - 7) = 15/2 - 35y/8 + 7 = (60 - 35y + 56)/8 = (116 - 35y)/8

The inequality becomes: (35 + 45y)/6 <= (116 - 35y)/8

Step 2: Clear the fractions by multiplying both sides of the inequality by the least common denominator (LCD) of 6 and 8, which is 24:

24 * [(35 + 45y)/6] <= 24 * [(116 - 35y)/8]

4(35 + 45y) <= 3(116 - 35y)

Step 3: Expand and simplify:

140 + 180y <= 348 - 105y

Step 4: Combine like terms:

180y + 105y <= 348 - 140

285y <= 208

Step 5: Divide both sides by 285 to isolate y:

y <= 208/285

This is the simplified solution for the inequality 5/6(7+9y) <= 7 1/2 - 7/8(5y-8).