# How do you solve abs(5.2x+7)=3.8?

Apr 3, 2017

$x = - \frac{8}{13} , - \frac{27}{13}$

#### Explanation:

CASE 1. $\textcolor{red}{5.2 x + 7 \ge 0}$

if
$5.2 x + 7 \ge 0$
$i . e . x \ge - \frac{7}{5.2}$ or $x \ge - \frac{35}{26}$

then
$| 5.2 x + 7 | = 5.2 x + 7$
because the modulus of a positive number is the number itself.

$\therefore$ in this case $5.2 x + 7 = 3.8$ $\implies 5.2 x = - 3.2$
$\implies x = - \frac{3.2}{5.2} = \textcolor{red}{- \frac{8}{13}}$

CASE 2. $\textcolor{red}{5.2 x + 7 < 0}$

if
$5.2 x + 7 < 0$
$i . e . x < - \frac{7}{5.2}$ or $x < - \frac{35}{26}$

then
$| 5.2 x + 7 | = - \left(5.2 x + 7\right) = - 5.2 x - 7$
because the modulus of a negative number is negative of the number or in other words modulus of a negative number is obtained by multiplying the number with $- 1$.

$e . g . - 2 < 0 \implies | - 2 | = - \left(- 2\right) \mathmr{and} - 1 \cdot \left(- 2\right) = 2$

$\therefore$ in this case $- 5.2 x - 7 = 3.8$ $\implies - 5.2 x = 10.8$
$\implies x = - \frac{10.8}{5.2} = \textcolor{red}{- \frac{27}{13}}$

Hence, $x = \textcolor{red}{- \frac{8}{13}} \mathmr{and} \textcolor{red}{- \frac{27}{13}}$.