Question

1)x+8 3/7=9 2)3/4*(x-1/4)=1 5/16 3)0,4*(7,3+x)=5,6

Answer 1

Х+8 3/7=9     х=9-8 3/7   х=4/7

3/4(х-1/4) =1 5/16   х-1/4= 15/16:3/4   х-1/4=5/4     х= 5/4+1/4  х=6/4=3/2=1 1/2

0,4(7,3+х)=5,6  7,3+х=5,6:0,4;  7,3+х=14   х=14-7,3=6,7

Answer 2

Let's solve each of the equations step by step:

1. x + 8 3/7 = 9

To solve this equation, we need to isolate the variable x. We can start by subtracting 8 3/7 from both sides:

x + 8 3/7 - 8 3/7 = 9 - 8 3/7

x = 9 - 8 3/7

Now, we need to convert the mixed number 8 3/7 to an improper fraction. To do that, we multiply the whole number (8) by the denominator (7) and add the numerator (3):

x = 9 - (8 * 7 + 3)/7

x = 9 - (56 + 3)/7

x = 9 - 59/7

Next, we can simplify the fraction by finding a common denominator:

x = (63/7 - 59/7)

x = 4/7

Therefore, the solution to the equation is x = 4/7.

2. 3/4 * (x - 1/4) = 1 5/16

To solve this equation, we'll begin by simplifying the left side. We can distribute the 3/4 to the terms inside the parentheses:

(3/4) * x - (3/4) * (1/4) = 1 5/16

3/4 * x - 3/16 = 1 5/16

Next, we want to isolate the variable x. We can start by subtracting 3/16 from both sides:

3/4 * x - 3/16 - 3/16 = 1 5/16 - 3/16

3/4 * x - 6/16 = 1

Now, let's simplify the fractions:

3/4 * x - 3/8 = 1

To eliminate the fraction, we can multiply the entire equation by the reciprocal of the coefficient of x, which is 4/3:

(4/3) * (3/4 * x - 3/8) = (4/3) * 1

x - 1/2 = 4/3

Next, we'll isolate x by adding 1/2 to both sides:

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

x = 4/3 + 1/2

To add these fractions, we need a common denominator:

x = (8/6 + 3/6)

x = 11/6

Therefore, the solution to the equation is x = 11/6.

3. 0.4 * (7.3 + x) = 5.6

To solve this equation, we can start by simplifying the left side:

0.4 * (7.3 + x) = 5.6

Next, we can distribute 0.4 to the terms inside the parentheses:

0.4 * 7.3 + 0.4 * x = 5.6

2.92 + 0.4 * x = 5.6

Now, let's isolate x by subtracting 2.92 from both sides:

0.4 * x = 5.6 - 2.92

0.4 * x = 2.68

To solve for x, we divide both sides by 0.4:

x = 2.68 / 0.4

x = 6.7

Therefore, the solution to the equation is x = 6.