# How do you solve  2(x + 5) > 8x – 8?

May 8, 2015

To solve for this problem, you can do it similar to any regular function, but this time with the inequality ($>$, which is greater than, or $<$, which is less than). First, begin by multiplying the factor out with $2$:

$2 \left(x + 5\right) > 8 x - 8 \implies 2 x + 10 > 8 x - 8$

Then solve for $x$ by method of subtracting the terms:

$2 x + 10 > 8 x - 8 \implies$subtract $2 x$ and $- 8$ to both sides,

$18 > 6 x \implies$divide $6$ to both sides,

$3 > x$, $\implies x < 3$

Thus, for the inequality of the equation to work, the variable $x$ must be less than (and not equal to) $3$, unless it is $x \le 3$ (note the symbol $\le$ vs. $<$).

Now there will be cases where you may have to switch the inequity. If you end up with the step

$18 > - 6 x$ or any other negative number multiplied by $x$,

then you have to switch the $>$ to $<$, since the result is a negative number:

$18 > - 6 x \implies$divide the -6 on both sides and switch the inequity,

$- 3 < x$ $\implies x > - 3$.

Hope some of the key points help out when doing inequalities!