Question

1). (9 2/3-х):3,5=17/35:1,02. 2). (6,5+х):0,475=1 11/19:3/28. ​

Answer 1

1. 9 2/3 -x = 50/51*17/35*3,5
29/3-x=50/3*1/35*7/2
29/3-x=25/3*1/5
29/3-x=5/3
-x=5/3-29/3
-x=-8
x=8

Answer 2

To solve the equations, let's simplify each expression step by step:

1. (9 2/3 - x) / 3.5 = 17/35 / 1.02

First, let's convert the mixed number 9 2/3 into an improper fraction:

9 2/3 = (3 * 9 + 2) / 3 = 29/3

Now, we can rewrite the equation as:

(29/3 - x) / 3.5 = 17/35 / 1.02

To simplify further, let's convert the division by 3.5 into multiplication by its reciprocal:

[(29/3 - x) * (1/3.5)] = 17/35 / 1.02

Simplifying the left side:

(29/3 - x) * (1/3.5) = 17/35 / 1.02 (29/3 - x) * (1/3.5) = (17/35) * (1/1.02)

Multiplying both sides by 3.5 to eliminate the fraction:

(29/3 - x) = (17/35) * (1/1.02) * 3.5

Simplifying the right side:

(29/3 - x) = (17/35) * (3.5/1.02) (29/3 - x) = (17 * 3.5) / (35 * 1.02)

Now, let's calculate the right side:

(29/3 - x) = (59.5) / (35 * 1.02) (29/3 - x) = 59.5 / 35.7

Dividing 59.5 by 35.7:

(29/3 - x) = 1.6667

To isolate x, let's subtract 29/3 from both sides:

• x = 1.6667 - 29/3

To simplify further, let's convert 1.6667 into a fraction:

1.6667 = 5/3

Substituting back:

• x = 5/3 - 29/3
• x = -24/3
• x = -8

Therefore, the solution to the first equation is x = -8.

2. (6.5 + x) / 0.475 = (1 11/19) / (3/28)

First, let's convert the mixed number 1 11/19 into an improper fraction:

1 11/19 = (19 * 1 + 11) / 19 = 30/19

Now, we can rewrite the equation as:

(6.5 + x) / 0.475 = (30/19) / (3/28)

To simplify further, let's convert the division by 0.475 into multiplication by its reciprocal:

[(6.5 + x) * (1/0.475)] = (30/19) / (3/28)

Simplifying the left side:

(6.5 + x) * (1/0.475) = (30/19) / (3/28) (6.5 + x) * (1/0.475) = (30/19) * (28/3)

Multiplying both sides by 0.475 to eliminate the fraction:

(6.5 + x) = (30/19) * (28/3) * 0.475

Simplifying the right side:

(6.5 + x) = (30 * 28 * 0.475) / (19 * 3)

Now, let's calculate the right side:

(6.5 + x) = 3.94

To isolate x, let's subtract 6.5 from both sides:

x = 3.94 - 6.5

x = -2.56

Therefore, the solution to the second equation is x = -2.56.