# How do you solve |-4x + 10| ≤ 46?

The solution is
For all values above 9 and less than or equal to 14, the relation is valid

#### Explanation:

$\left\mid - 4 x + 10 \right\mid \le 46$
$- 4 x + 10 \le 46$
$- 4 x \le 46 - 10$
$- 4 x \le 36$
$- x \le \frac{36}{4}$
$- x \le 9$
$x > 9$
or
$- 4 x + 10 \le - 46$
$- 4 x \le - 46 - 10$
$- 4 x \le - 56$
$4 x \le 56$
$x \le \frac{56}{4}$
$x \le 14$
The solution is
$x > 9 , x \le 14$
For all values above 9 and less than or equal to 14, the relation is valid

Aug 6, 2018

The solution is $x \in \left[- 9 , 14\right]$

#### Explanation:

The inequality is

$| - 4 x + 10 | \le 46$

The solution is

$\left\{\begin{matrix}4 x - 10 \le 46 \\ - 4 x + 10 \le 46\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}4 x \le 46 + 10 \\ 4 x \ge 10 - 46\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}4 x \le 56 \\ 4 x \ge - 36\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x \le \frac{56}{4} \\ x \ge - \frac{36}{4}\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x \le 14 \\ x \ge - 9\end{matrix}\right.$

The solution is

$x \in \left[- 9 , 14\right]$

graph{|4x-10|-46 [-105.4, 105.4, -52.7, 52.7]}