Answer
$x=3$
Work Step by Step
The given equation is
$\Rightarrow |2x−19|=4x+1$
Write related linear equations.
$\Rightarrow 2x−19=4x+1$ or $2x−19=−(4x+1)$
Solve the first equation.
$\Rightarrow 2x-19=4x+1$
Add $-1-2x$ to each side.
$\Rightarrow 2x-19-1-2x=4x+1-1-2x$
Simplify.
$\Rightarrow -20=2x$
Divide each side by $2$.
$\Rightarrow -\frac{20}{2}=\frac{2x}{2}$
Simplify.
$\Rightarrow -10=x$
Solve the second equation.
$\Rightarrow 2x−19=−(4x+1)$
Clear the parentheses.
$\Rightarrow 2x−19=−4x-1$
Add $4x+19$ to each side.
$\Rightarrow 2x−19+4x+19=−4x-1+4x+19$
Simplify.
$\Rightarrow 6x=18$
Divide each side by $6$.
$\Rightarrow \frac{6x}{6}=\frac{18}{6}$
Simplify.
$\Rightarrow x=3$
Check $x=-10$
$\Rightarrow |2(-10)−19|=4(-10)+1$
$\Rightarrow |-20−19|=-40+1$
$\Rightarrow |-39|=-39$
$\Rightarrow 39=-39$
False.
Check $x=3$
$\Rightarrow |2(3)−19|=4(3)+1$
$\Rightarrow |6−19|=12+1$
$\Rightarrow |-13|=13$
$\Rightarrow 13=13$
True.
Hence, the solution is $x=3$.
