Answer
$\left \{-4,-\frac{6}{11}\right \}$.
Work Step by Step
$\Rightarrow |4x-3|=|7x+9|$
Rewrite the equation without absolute value bars.
$\Rightarrow 4x-3= 7x+9 $. or $ 4x-3 =-\left ( 7x+9 \right ) $.
Clear the parentheses.
$\Rightarrow 4x-3= 7x+9 $. or $ 4x-3 =-7x-9 $.
Add $3$ to both sides of each equation.
$\Rightarrow 4x-3+3= 7x+9+3 $. or $ 4x-3+3 =-7x-9+3 $.
Simplify.
$\Rightarrow 4x= 7x+12 $. or $ 4x =-7x-6 $.
Subtract $7x$ from both sides of the first equation and add $7x$ to both sides of the second equation.
$\Rightarrow 4x-7x= 7x+12-7x $. or $ 4x+7x =-7x-6+7x $.
Simplify.
$\Rightarrow -3x= 12 $. or $ 11x =-6 $.
Isolate $x$ form both sides of each equation.
$\Rightarrow x= \frac{12}{-3} $. or $ x =\frac{-6}{11} $.
Simplify.
$\Rightarrow x=-4 $. or $ x =-\frac{6}{11} $.
Check $x=-4$
$\Rightarrow |4(-4)-3|=|7(-4)+9|$
$\Rightarrow |-16-3|=|-28+9|$
$\Rightarrow |-19|=|-19|$
$\Rightarrow 19=19$ True.
Check $x=-4$
$\Rightarrow |4(-\frac{6}{11})-3|=|7(-\frac{6}{11})+9|$
$\Rightarrow |-\frac{24}{11}-3|=|-\frac{42}{11}+9|$
$\Rightarrow |\frac{-24-33}{11}|=|\frac{-42+99}{11}|$
$\Rightarrow |\frac{-57}{11}|=|\frac{-57}{11}|$
$\Rightarrow \frac{57}{11}=\frac{57}{11}$ True.
Hence, the solution set is $\left \{-4,-\frac{6}{11}\right \}$.
