Question

4/7(0,56-4.2х)+0,4=5/13(0,52-6,5х) дроби

Answer 1

4/7(56/100-42x/10)+4/10=5/13(52/100-65x/10)
4/7(14/25-21x/5)+2/5=5/13(13/25-13x/2)
8/25-12x/5+2/5=1/5-5x/2
-12x/5+5x/2=1/5-8/25-2/5
-24x/10+25x/10=5/25-8/25-10/25
x/10=-13/25
x=-13/25*10
x= -26/5= -5 1/5 или -5,2

Answer 2

Раскрываем скобки
4/7*0,56-4/7*4,2х+0,4=5/13*0,52-5/13*6,5х
0,32-2,4х+0,4=0,2-2,5х
-2,4х+2,5х=0,2-0,4-0,32
0,1х=-0,52
х=-0,52/0,1
х=-5,2

и вот проверка
4/7(0,56-4,2*(-5,2)+0,4=5/13(0,52-6,5*(-5,2))
4/7*22,4+0,4=5/13*34,32
12,8+0,4=13,2
13,2=13,2

Answer 3

To solve the equation involving fractions, we need to find the value of 'x' that satisfies the equation. Let's go step by step to solve it:

1. Distribute the fractions and simplify the expressions on both sides of the equation.

For the left side: 4/7(0.56 - 4.2x) + 0.4 = (4/7 * 0.56) - (4/7 * 4.2x) + 0.4 = 0.32 - (2.4/7)x + 0.4 = 0.72 - (2.4/7)x

For the right side: 5/13(0.52 - 6.5x) = (5/13 * 0.52) - (5/13 * 6.5x) = 0.2 - (2.5/13)x

The equation now becomes: 0.72 - (2.4/7)x = 0.2 - (2.5/13)x

2. Move all the terms containing 'x' to one side of the equation and the constant terms to the other side.

Add (2.5/13)x to both sides: 0.72 - (2.4/7)x + (2.5/13)x = 0.2

Now, let's find a common denominator for the fractions containing 'x' to combine them: The common denominator for 7 and 13 is 7 * 13 = 91.

So, rewrite the equation with a common denominator: (91/91) * 0.72 - (13/13 * 2.4/7)x + (7/7 * 2.5/13)x = 0.2

Now, the equation becomes: (65.52/91) - (31.2/91)x + (17.5/91)x = 0.2

3. Combine the 'x' terms and constant terms:

(-31.2/91 + 17.5/91)x = 0.2 - 65.52/91

4. Find the common denominator for the constant terms on the right side:

The common denominator for 1 and 91 is 91.

Now, rewrite the equation with a common denominator: (-31.2/91 + 17.5/91)x = (91/91) * 0.2 - 65.52/91

(-31.2/91 + 17.5/91)x = (18.2/91) - (65.52/91)

5. Combine the constant terms on the right side:

(-31.2/91 + 17.5/91)x = (-47.32/91)

6. Now, solve for 'x':

x = (-47.32/91) / ((-31.2/91 + 17.5/91))

x = (-47.32/91) / (-13.7/91)

x = (-47.32/91) * (-91/13.7)

x = 3.28

So, the value of 'x' that satisfies the equation is approximately x = 3.28.