Question

Решите уравнения : 1) (1 7/8×х-2 1/3)×24=4 2) 3 1/3:(3/7×х-13/15)=1 9/16

Answer 1

Ответ:

Пошаговое объяснение:

1) (1 7/8×х-2 1/3)×24=4

1 7/8x-2 1/3=4/24=1/6

1 7/8x=1/6+2 1/3

1 7/8x=1/6+2 2/6

1 7/8x=2 1/2

x=2 1/2:1 7/8=5/2*8/15

x=4/3=1 1/3

2) 3 1/3:(3/7×х-13/15)=1 9/16

3/7x-13/15=3 1/3:1 9/16

3/7x-13/15=10/3*16/25

3/7x-13/15=32/15

3/7x=32/15+13/15

3/7x=45/15=3

x=3*7/3

x=7

Answer 2

First, let's simplify the left-hand side of the equation:

(1 7/8 × x - 2 1/3) × 24

= (15/8 × x - 7/3) × 24 (convert mixed numbers to improper fractions)

= 15/8 × 24x - 7/3 × 24 (distribute the multiplication)

= 45/2 x - 56 (multiply fractions and simplify)

Now we have the equation:

45/2 x - 56 = 4

To solve for x, we can isolate the x term by adding 56 to both sides and then multiplying both sides by 2/45:

45/2 x - 56 + 56 = 4 + 56

45/2 x = 60

x = 80/3

Therefore, the solution is x = 80/3.

First, let's simplify the left-hand side of the equation:

3 1/3 : (3/7 × x - 13/15)

= 10/3 : (3/7 × x - 13/15) (convert mixed numbers to improper fractions)

= 10/3 × (7/3 × x - 13/45) (invert and multiply by the reciprocal)

= 70/9 × x - 130/135 (distribute the multiplication and simplify)

Now we have the equation:

70/9 × x - 130/135 = 1 9/16

To solve for x, we can isolate the x term by adding 130/135 to both sides and then multiplying both sides by 9/70:

70/9 × x - 130/135 + 130/135 = 1 9/16 + 130/135

70/9 × x = 247/45

x = 63/10

Therefore, the solution is x = 63/10.