Question

1) 4(0,6x-0,3)-3(0,7x-0,1)=0 2) 5(0,14-025x)+3(0,3x+0,1)=0 3) (1 3 - 2 3):1 3                                     4      8     5 4) (1 7 + 3 1)*5       15       3 12 5) (4 1 - 2 5)*(-1 3)         8     16      29

Answer 1

1) 4(0,6x-0,3)-3(0,7x-0,1)=0
2,4x-1,2-2,1x+0,3=0
0,3x-0,9=0
0,3x=0,9
x=3
2) 5(0,14-0,25x)+3(0,3x+0,1)=0
0,7-1,25x+0,9x+0,3=0
-1,25x+0,9x=-0,7-0,3
-0,35x=-1
x=2,857 (если округлить, то получится 3)
3) $(1 \frac{3}{4}-2 \frac{3}{8}):1 \frac{3}{5}$
1)  $1\frac{3}{4} -2 \frac{3}{8}= \frac{7}{4}- \frac{19}{8} \frac{28-19}{8}= \frac{9}{8}$
2)  $\frac{9}{8}: \frac{8}{5}= \frac{9*5}{8*8} = \frac{45}{64}$
4)  $(1 \frac{7}{15}+3 \frac{1}{3})* \frac{5}{12}$
1) $1 \frac{7}{15}+ 3\frac{1}{3}= \frac{22}{15}+ \frac{10}{3}= \frac{22+50}{15} = \frac{75}{15}$
2)  $\frac{75}{15}* \frac{5}{12}= \frac{75*5}{15*12}= \frac{25}{12} = 2\frac{1}{12}$
5) $(4 \frac{1}{8}-2 \frac{5}{16})*(- \frac{13}{29} )$
1)  $4 \frac{1}{8}-2 \frac{5}{16} = \frac{33}{8}- \frac{37}{16}= \frac{66-37}{16} = \frac{29}{16}$
2)  $\frac{29}{16}*(- \frac{13}{29})=- \frac{29*13}{16*29}= - \frac{13}{16}$

Answer 2

Let's solve the given equations and perform the operations step by step:

1. 4(0.6x - 0.3) - 3(0.7x - 0.1) = 0

Expanding the terms: 2.4x - 1.2 - 2.1x + 0.3 = 0

Combining like terms: (2.4x - 2.1x) + (-1.2 + 0.3) = 0

0.3x - 0.9 = 0

Adding 0.9 to both sides: 0.3x = 0.9

Dividing by 0.3: x = 3

So the solution to the equation is x = 3.

2. 5(0.14 - 0.25x) + 3(0.3x + 0.1) = 0

Expanding the terms: 0.7 - 1.25x + 0.9x + 0.3 = 0

Combining like terms: (-1.25x + 0.9x) + (0.7 + 0.3) = 0

-0.35x + 1 = 0

Subtracting 1 from both sides: -0.35x = -1

Dividing by -0.35: x = 2.857 (rounded to three decimal places)

So the solution to the equation is x = 2.857.

3. (1/3) ÷ (1/3)

When dividing fractions, we can multiply the first fraction by the reciprocal of the second fraction: (1/3) * (3/1) = 1

So the result is 1.

4. (1/7 + 3/1) * 5

First, let's find the common denominator, which is 7: (1/7 + 21/7) * 5

Combining the fractions: (22/7) * 5

Multiplying the numerators: 22 * 5 = 110

Multiplying the denominators: 7

So the result is 110/7, which can be simplified as 15 5/7.

5. (4/1 - 2/5) * (-1/3)

First, let's find the common denominator, which is 5: (20/5 - 2/5) * (-1/3)

Combining the fractions: (18/5) * (-1/3)

Multiplying the numerators: 18 * -1 = -18

Multiplying the denominators: 5 * 3 = 15

So the result is -18/15, which can be simplified as -6/5 or -1.2.