An algebra problem by A Former Brilliant Member

$\ |2x-5|=21$

$2x-5=21$ or $2x-5=-21$

Solving the first linear equation. We have,

$2x=21+5$

$2x=26$

$x=13$

Solving the second linear equation. We have,

$2x-5=-21$

$2x=-21+5$

$2x=-16$

$x=-8$

$\large \therefore$ $\boxed{\text{The solutions are 13 and -8.}}$

$|2x-5|=21 \implies \begin{cases} 2x-5 = 21 & \text{for } x > \dfrac 52 & \implies x = 13 > \dfrac 52 \\ -2x+5 = 21 & \text{for } x < \dfrac 52 & \implies x = -8 < \dfrac 52 \end{cases}$

Therefore the solutions are 13 and -8 .

$|2x - 5| = 21$

$2x - 5 = -21$ or $2x - 5 = 21$

Now,

$2x - 5 = -21$

Add $5$ to both sides,

$2x - 5 + 5 = -21 + 5$

$2x = -16$

Divide $-16$ with $2,$

$x =$ $\dfrac{-16}{2}$

$x = -8$

Again,

$2x - 5 = 20$

Add $5$ to both sides,

$2x - 5 + 5 = 20 + 5$

$2x = 26$

Divide $26$ with $2,$

$x =$ $\dfrac{26}{2}$

$x = 13$

Therefore, $\color{#3D99F6} \boxed {x = -8}$ and $\color{#69047E} \boxed{x =13}$