# How do you solve 12x – 5x < 6(x + 7)?

May 3, 2018

$x < 42$

#### Explanation:

$\text{simplify left side and distribute parenthesis}$

$\Rightarrow 7 x < 6 x + 42 \leftarrow \textcolor{b l u e}{\text{subtract 6x from both sides}}$

$\Rightarrow x < 42 \text{ is the solution}$

$x \in \left(- \infty , 42\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

May 3, 2018

You get $x < 42$

#### Explanation:

I would simplify the left side, since $12 - 5 x = 7 x$.

Therefore $7 x < 6 \left(x + 7\right)$
Now $6 \left(x + 7\right)$ is the same as multiplying each term in the parenthesis with the number outside, i.e.
$6 \left(x + 7\right) = 6 x + 6 \cdot 7 = 6 x + 42$
Therefore we have
$7 x < 6 x + 42$

So 7 of something should be smaller than 6 of something pluss 42.

I hope it then is easy to see that this is fulfilled if 1 of that something is smaller than 42,
i.e.
$x < 42$

Normally we would do it this way, deducting the same amount from each side:
$7 x - 6 x < 6 x + 42 - 6 x$
Which would give
$x < 42$