Question

(1 5/18-x)+5/9=2/310-(x-1 1/2)=7 5/6(x+2/5)+1 2/3=5 11/15​

Answer 1

Ответ:

13/18

3

29.6

Объяснение:

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Answer 2

To solve the equation:

(1 5/18 - x) + 5/9 = 2/310 - (x - 1 1/2) = 7 5/6(x + 2/5) + 1 2/3 = 5 11/15

we can break it down into three separate equations:

1. (1 5/18 - x) + 5/9 = 2/310
2. -(x - 1 1/2) = 7 5/6(x + 2/5)
3. 7 5/6(x + 2/5) + 1 2/3 = 5 11/15

Let's solve each equation step by step:

Equation 1: (1 5/18 - x) + 5/9 = 2/310

First, simplify the left side of the equation:

1 5/18 - x + 5/9 = 2/310

To clear fractions, multiply both sides by 18 * 9 * 310 (the least common multiple of the denominators):

(1 5/18 - x + 5/9) * (18 * 9 * 310) = (2/310) * (18 * 9 * 310)

Now, calculate the values on both sides:

(1 5/18 - x) * (18 * 9 * 310) + (5/9) * (18 * 9 * 310) = 2 * 18 * 9 (1 5/18 - x) * 56160 + 10 * 310 = 2 * 18 * 9 (1 5/18 - x) * 56160 + 3100 = 324

Now, subtract 3100 from both sides:

(1 5/18 - x) * 56160 = 324 - 3100 (1 5/18 - x) * 56160 = -2776

Now, divide both sides by 56160 to solve for x:

1 5/18 - x = -2776 / 56160

To make calculations easier, convert 1 5/18 to an improper fraction:

23/18 - x = -2776 / 56160

Now, subtract 23/18 from both sides:

• x = -2776 / 56160 - 23/18

To subtract fractions, find a common denominator, which in this case is 56160 * 18:

• x = (-2776 * 18 - 23 * 56160) / (56160 * 18)

Now, calculate the numerator:

• x = (-49968 - 1327488) / 1010880

• x = -1377456 / 1010880

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 48:

• x = (-28680) / (21060)

• x = -14340 / 10530

• x = -4780 / 3510

Now, you can simplify this fraction further if needed.

Equation 2: -(x - 1 1/2) = 7 5/6(x + 2/5)

First, distribute the 7 5/6 on the right side:

-(x - 1 1/2) = 7 5/6 * x + 7 5/6 * 2/5

Now, simplify the right side:

-(x - 1 1/2) = (7x/6) + (7/6) * (2/5)

To subtract 1 1/2 from both sides, you can convert it to an improper fraction:

-[(x - 3/2)] = (7x/6) + (7/6) * (2/5)

Now, distribute the negative sign on the left side:

-1(x - 3/2) = (7x/6) + (7/6) * (2/5)

Now, simplify both sides:

-(x - 3/2) = (7x/6) + (7/6) * (2/5)

-1(x) + 1(3/2) = (7x/6) + (7/6) * (2/5)

Now, subtract (3/2) from both sides:

• x + 3/2 = (7x/6) + (7/6) * (2/5)

Now, to clear fractions, find a common denominator on the right side, which is 6 * 5:

• x + 3/2 = (35x/30) + (14/30)

Now, subtract (35x/30) from both sides:

• x + 3/2 - (35x/30) = 14/30

To simplify further, find a common denominator of 30:

• 30x + 45 - 35x = 14/30

Now, subtract 45 from both sides:

• 30x - 35x = 14/30 - 45/30

• 65x = -31/30

Now, divide both sides by -65 to solve for x:

x = (-31/30) / (-65)

x = (31/30) / 65

x = 31 / (30 * 65)

Now, simplify the fraction if needed.

Equation 3: 7 5/6(x + 2/5) + 1 2/3 = 5 11/15

First, simplify the left side of the equation:

7 5/6(x + 2/5) + 1 2/3 = 5 11/15

Now, convert all the mixed numbers to improper fractions:

(37/6)(x + 2/5) + (5/3) = (86/15)

Now, distribute (37/6) on the left side:

(37/6)(x) + (37/6)(2/5) + (5/3) = (86/15)

Now, simplify the fractions:

(37/6)(x) + (37/15) + (5/3) = (86/15)

Now, subtract (5/3) from both sides:

(37/6)(x) + (37/15) = (86/15) - (5/3)

Now, find a common denominator on the right side, which is 15:

(37/6)(x) + (37/15) = (86/15) - (25/15)

Now, subtract the fractions on the right side:

(37/6)(x) + (37/15) = 61/15

Now, subtract (37/15) from both sides:

(37/6)(x) = 61/15 - (37/15)

(37/6)(x) = 24/15

Now, divide both sides by (37/6) to solve for x:

x = (24/15) / (37/6)

x = (24/15) * (6/37)

x = (8/5) * (2/37)

x = 16/185

So, the solution to the equation system is:

x ≈ 16/185