# Question #60f48

Aug 25, 2016

$x > - 1$

#### Explanation:

We can solve an inequality like this if we remember the following rules:

• We can add or subtract any real number to both sides of an inequality without changing its direction.
E.g. $x < y \implies x + 1 < y + 1$
• We can multiply both sides of an inequality by any positive real number without changing its direction.
E.g $x < y \implies 4 x < 4 y$
• We can multiply both sides of an inequality by any negative real number if we change its direction.
E.g $x < y \implies - 2 x > - 2 y$

With those in mind, we can use those to isolate $x$:

$- 3 x + 8 < 11$

$\implies - 3 x + 8 - 8 < 11 - 8$

$\implies - 3 x < 3$

$\implies - 3 x \cdot - \frac{1}{3} > 3 \cdot - \frac{1}{3}$

$\therefore x > - 1$