Question

4/х-3>6/х. 3/х+3>2/х

Answer 1

$1) \frac{-2}{3}$

$2) x$ или $x>0$

Answer 2

To solve the inequalities, we can follow these steps for each one:

1. 4/x - 3 > 6/x

First, let's find a common denominator for the fractions, which is x in this case:

4/x - 3x/x > 6/x

Now, combine the fractions:

(4 - 3x)/x > 6/x

Now, multiply both sides by x to eliminate the denominators. Remember to reverse the inequality sign when multiplying by a negative number (in this case, x can be positive or negative):

(4 - 3x) > 6

Now, solve for x:

4 - 3x > 6

Subtract 4 from both sides:

-3x > 2

Finally, divide by -3 (remember to reverse the inequality sign):

x < -2/3

So, the solution to the first inequality is x < -2/3.

2. 3/x + 3 > 2/x

Follow the same steps as before, finding a common denominator, combining fractions, and solving for x:

3/x + 3x/x > 2/x

(3 + 3x)/x > 2/x

Multiply both sides by x:

3 + 3x > 2

Subtract 3 from both sides:

3x > -1

Now, divide by 3:

x > -1/3

So, the solution to the second inequality is x > -1/3.