Question

36. 1) 7,5х = 35,88: 2) 1,25х = 40; 3) 7 2/3x = 9/46

Answer 1

$1)\;7,5x=35,88\\7\frac5{10}x=35\frac{88}{100}\\\\7\frac12x=35\frac{22}{25}\\\\\frac{15}2x=\frac{897}{25}\\\\x=\frac{897}{25}:\frac{15}2=\frac{897}{25}\cdot\frac2{15}=\frac{299}{25}\cdot\frac2{5}=\frac{598}{125}=4\frac{98}{125}$

$2)\;1,25x=40\\1\frac14x=40\\\frac54x=40\\x=40:\frac54=40\cdot\frac45=8\cdot4=32\\\\3)\;7\frac23x=\frac9{46}\\\frac{23}{3}x=\frac9{46}\\x=\frac9{46}:\frac{23}3=\frac9{46}\cdot\frac3{23}=\frac{27}{1058}$

Answer 2

Let's solve the equations step by step:

1. 7.5x = 35.88

To solve for x, we need to isolate it on one side of the equation. Divide both sides of the equation by 7.5:

(7.5x)/7.5 = 35.88/7.5

x = 4.784

Therefore, the solution to the first equation is x = 4.784.

2. 1.25x = 40

Divide both sides of the equation by 1.25:

(1.25x)/1.25 = 40/1.25

x = 32

So, the solution to the second equation is x = 32.

3. 7 2/3x = 9/46

To solve this equation, we need to convert the mixed number 7 2/3 into an improper fraction. Multiply the whole number (7) by the denominator of the fraction (3) and add the numerator (2). Then, place the sum over the denominator:

7 2/3 = (7 * 3 + 2)/3 = 23/3

Now we can rewrite the equation:

(23/3)x = 9/46

To isolate x, we need to multiply both sides of the equation by the reciprocal of (23/3), which is (3/23):

(3/23)(23/3)x = (3/23)(9/46)

x = (27/46)

The solution to the third equation is x = 27/46.

In summary, the solutions to the given equations are:

1. x = 4.784
2. x = 32
3. x = 27/46