Question

Нок (14;26)-(11×x-23)=нод (320;280)

Answer 1

Нок (14;26) - (11 × x - 23 ) = Нод (320;280)

182 - (11 × x - 23)= 40

182 - 40=142

142+23=165

x=165 : 11

x= 15

Answer 2

To find the value of 'x' in the equation "Нок (14;26) - (11×x-23) = нод (320;280)", we first need to calculate the least common multiple (LCM) of 14 and 26, as well as the greatest common divisor (GCD) of 320 and 280.

Step 1: Find the LCM of 14 and 26 The LCM of two numbers is the smallest multiple that is divisible by both numbers. To calculate the LCM of 14 and 26, we can use the formula:

LCM(a, b) = (a * b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of 'a' and 'b'.

Step 2: Find the GCD of 320 and 280 To find the GCD of 320 and 280, we can use a common algorithm like the Euclidean algorithm.

GCD(320, 280) = 40

Step 3: Calculate the LCM of 14 and 26 LCM(14, 26) = (14 * 26) / GCD(14, 26) = (14 * 26) / 2 = 364

Now we have the values: LCM(14, 26) = 364 and GCD(320, 280) = 40.

Step 4: Solve the equation for 'x' Now, we can replace the Нок (14;26) and нод (320;280) with their respective values:

364 - (11x - 23) = 40

Next, let's simplify the equation:

364 - 11x + 23 = 40

Combine the constants:

387 - 11x = 40

Now, isolate 'x' on one side of the equation:

-11x = 40 - 387 -11x = -347

Finally, solve for 'x':

x = -347 / -11 x = 31.545

So, the value of 'x' is approximately 31.545.