Question

1-5x < -10 13x + 2 > 5

Answer 1

Ответ:

1.

$x > \frac{11 }{5} \\ x > \frac{3}{13}$

Answer 2

Let's solve these two inequalities separately:

1. $1 - 5x < -10$

First, add 5x to both sides of the inequality:

$1 - 5x + 5x < -10 + 5x$

This simplifies to:

$1 < -10 + 5x$

Now, subtract 10 from both sides:

$1 - 10 < 5x$

This simplifies to:

$-9 < 5x$

Finally, divide both sides by 5 (remember to reverse the inequality when dividing by a negative number):

$\frac{-9}{5} > x$

So, the solution to the first inequality is $x > \frac{-9}{5}$.

2. $13x + 2 > 5$

First, subtract 2 from both sides of the inequality:

$13x + 2 - 2 > 5 - 2$

This simplifies to:

$13x > 3$

Now, divide both sides by 13:

$\frac{13x}{13} > \frac{3}{13}$

This simplifies to:

$x > \frac{3}{13}$

So, the solution to the second inequality is (x > \frac{3}{13}.

In summary, the solution to the system of inequalities is:

$\frac{-9}{5} < x$ and $x > \frac{3}{13}$