Question

А)(1-5/9 х):1/3=3/5 Б) 5/6 х-1/4 х-2/9 х-3/8=1/24 С решением!

Answer 1

$a)1 - \frac{5}{9} x = \frac{3}{5} \times \frac{1}{3} = \frac{1}{5} \\ \frac{5}{9} x = 1 - \frac{1}{5} = \frac{5}{5} - \frac{1}{5} = \frac{4}{5}$

$x = \frac{4}{5} \div \frac{5}{9} = \frac{4}{5} \times \frac{9}{5} \\ x = \frac{36}{25} = 1 \frac{11}{25}$

Б)

$\frac{5}{6} x - \frac{1}{4} x - \frac{2}{9} x - \frac{3}{8} = \frac{1}{24} \\ \frac{5}{6} x - \frac{1}{4} x - \frac{2}{9} x =$

$= \frac{30}{36}x - \frac{9}{36}x - \frac{8}{36}x = \frac{13}{36} x$

$\frac{13}{36} x - \frac{3}{8} = \frac{1}{24} \\ \frac{13}{36} x = \frac{1}{24} + \frac{3}{8} = \frac{1}{24} + \frac{9}{24} = \frac{10}{24}$

$= \frac{5}{12}$

$x = \frac{5}{12}$

$x = \frac{5}{12} \div \frac{13}{36} = \frac{5}{12} \times \frac{36}{13} = \frac{15}{13} = \\ = 1 \frac{2}{13}$

Answer 2

А) Let's solve equation A step by step:

(1 - (5/9)x) / (1/3) = 3/5

To get rid of the fraction in the denominator, we can multiply both sides of the equation by its reciprocal:

(1 - (5/9)x) * (3/1) = 3/5 * (3/1)

Simplifying further:

3(1 - (5/9)x) = 9/5

Distribute the 3 on the left side:

3 - (15/9)x = 9/5

To eliminate the fraction, multiply through by the common denominator, which is 9:

27 - 15x = 9/5

Now, let's convert 9/5 to an improper fraction:

27 - 15x = 9/5 = 45/25

Multiplying through by 25 to clear the fraction:

25(27 - 15x) = 45

Simplifying:

675 - 375x = 45

Now, isolate the variable by moving the constant term to the other side:

-375x = 45 - 675

-375x = -630

Finally, divide both sides by -375 to solve for x:

x = (-630) / (-375)

x = 42/25

Therefore, the solution for equation A is x = 42/25.

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Б) Let's solve equation B step by step:

(5/6)x - (1/4)x - (2/9)x - (3/8) = 1/24

First, let's combine the x terms on the left side:

[(5/6)x - (1/4)x - (2/9)x] - (3/8) = 1/24

To simplify the expression in the brackets, we need to find a common denominator for 6, 4, and 9, which is 36:

[(20/36)x - (9/36)x - (8/36)x] - (3/8) = 1/24

Combining the x terms:

(20/36 - 9/36 - 8/36)x - (3/8) = 1/24

Simplifying further:

(3/36)x - (3/8) = 1/24

To eliminate the fractions, let's find a common denominator for 36, 8, and 24, which is 72:

(6/72)x - (27/72) = 3/72

Combining the fractions:

(6x - 27)/72 = 3/72

Now, cross-multiply:

6x - 27 = 3

To isolate the variable, let's move the constant term to the other side:

6x = 3 + 27

6x = 30

Finally, divide both sides by 6 to solve for x:

x = 30/6

x = 5

Therefore, the solution for equation B is x = 5.