The solution for absolute value equation |4x + 3| = 3 is:
[tex]x = \frac{-3}{2} \text{ and } x = 0[/tex]
Solution:
Absolute value equations are equations where the variable is within an absolute value operator
Given absolute value equation is:
[tex]|4x+3|=3[/tex]
The absolute value of a number depends on the number's sign
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |4x + 3|
For the Negative case we use -(4x + 3)
For the Positive case we use (4x + 3)
Solve the Negative Case
-(4x + 3) = 3
-4x - 3 = 3
-4x = 3 + 3
-4x = 6
Divide both sides by -4
[tex]x = \frac{-6}{4}\\\\x = \frac{-3}{2}[/tex]
Solve the Positive Case
(4x + 3) = 3
4x + 3 = 3
Move the constants to right
4x = 3 - 3
4x = 0
x = 0
Thus two solutions were found : [tex]x = \frac{-3}{2} \text{ and } x = 0[/tex]
