Question

1)4\7( икс-1 =2\7+ икс,2)4 2\3икс =5(1+0,1 икс),3) 5( икс-1,5)=4 2\3икс-8 3\14

Answer 1

Ответ:

Пошаговое объяснение:

1)4\7( икс-1 =2\7+ икс,

4/7x-4/7=2/7+x

4/7x-x=2/7+4/7

-3/7x=6/7

x=6/7:(-3/7)

x=6/7*(-7/3)

x=-2

2)4 2\3икс =5(1+0,1 икс),

4 2/3x=5+0.5x

4 2/3x-0.5x=5

4 2/3x-1/2x=5

4 4/6x-3/6x=5

4 1/6x=5

x=5:4 1/6

x=5*6/25

x=6/5=1 1/5

3) 5( икс-1,5)=4 2\3икс-8 3\14

5x-7.5=4 2/3x-8 3/14

5x-4 2/3x=7.5-8 3/14

5x-4 2/3x=7 1/2-8 3/14

1/3x=7 7/14-8 3/14

1/3x=10/14

x=10/14:1/2

x=10/14*2

x=10/7=1 3/7

Answer 2

To solve these equations, let's simplify and solve them step by step:

1. 4/7(x - 1) = 2/7 + x

First, let's clear the fraction by multiplying every term by the common denominator, which is 7: 7 * 4/7(x - 1) = 7 * 2/7 + 7 * x

Simplifying: 4(x - 1) = 2 + 7x

Expand the brackets: 4x - 4 = 2 + 7x

Move all terms with x to one side and constants to the other side: 4x - 7x = 2 + 4 -3x = 6

Divide both sides by -3: x = 6/-3 x = -2

Therefore, the solution to the equation is x = -2.

2. 4 2/3x = 5(1 + 0.1x)

Let's first convert the mixed number, 4 2/3, to an improper fraction: 4 2/3 = (4 * 3 + 2)/3 = 14/3

Now we can rewrite the equation as: 14/3x = 5(1 + 0.1x)

Distribute 5 to the terms inside the parentheses: 14/3x = 5 + 0.5x

Multiply every term by 3 to eliminate the fraction: 3 * (14/3x) = 3 * (5 + 0.5x)

Simplifying: 14x = 15 + 1.5x

Move all terms with x to one side and constants to the other side: 14x - 1.5x = 15 12.5x = 15

Divide both sides by 12.5: x = 15/12.5 x = 1.2

Therefore, the solution to the equation is x = 1.2.

3. 5(x - 1.5) = 4 2/3x - 8 3/14

Let's convert the mixed numbers to improper fractions: 4 2/3 = (4 * 3 + 2)/3 = 14/3 8 3/14 = (8 * 14 + 3)/14 = 115/14

Rewriting the equation with the improper fractions: 5(x - 1.5) = 14/3x - 115/14

Multiply every term by the common denominator, which is 42, to eliminate the fractions: 42 * 5(x - 1.5) = 42 * (14/3x) - 42 * (115/14)

Simplifying: 210(x - 1.5) = (14 * 14)x - 3 * 115

Expand and simplify: 210x - 315 = 196x - 345

Move all terms with x to one side and constants to the other side: 210x - 196x = -345 + 315 14x = -30

Divide both sides by 14: x = -30/14 x = -15/7

Therefore, the solution to the equation is x = -15/7 or approximately x = -2.1429.