Question

X/6 + 1/2 > X - 1/3​

Answer 1

X/6+1/2>x-1/3
x/6-x>-1/2-1/3
(x-6x)/6>-(3+2)/6
-5x>-5
x<1
Ответ: (-∞;1)

Answer 2

To solve the inequality X/6 + 1/2 > X - 1/3, we can simplify the equation and isolate the variable X.

First, let's find a common denominator for the fractions on both sides of the inequality. The common denominator in this case is 6:

(X/6) + (1/2) > X - (1/3)

Multiplying the first fraction by 1 to keep it unchanged, but with the denominator of 6:

(X/6) + (1/2) * (3/3) > X - (1/3)

(X/6) + (3/6) > X - (1/3)

Now, we can combine the fractions:

(X + 3)/6 > X - (1/3)

Next, we can eliminate the fraction on the right side by multiplying the whole inequality by 6:

6 * [(X + 3)/6] > 6 * [X - (1/3)]

(X + 3) > 6X - 2

Now, let's simplify the inequality:

X + 3 > 6X - 2

Subtracting X from both sides:

3 > 5X - 2

Adding 2 to both sides:

5 > 5X

Finally, dividing both sides by 5:

1 > X

So, the solution to the inequality X/6 + 1/2 > X - 1/3 is X < 1.