ANSWER
[tex]B. \: x = \frac{7}{6} [/tex]
EXPLANATION
The given absolute value equation is
[tex] |x + 3| = 7x - 4[/tex]
This implies that, either
[tex] x + 3= 7x - 4[/tex]
Or
[tex] - (x + 3)= 7x - 4[/tex]
[tex] - x - 3 = 7x - 4[/tex]
Group similar terms;
[tex]3 + 4 = 7x - x[/tex]
or
[tex] - 3 + 4 = 7x + x[/tex]
Simplify:
[tex]7 = 6x[/tex]
or
[tex]1 = 8x[/tex]
Solve for x.
[tex] x = \frac{7}{6} \: or \: x = \frac{1}{8} [/tex]
Check for extraneous solutions.
[tex]| \frac{7}{6} + 3| = 7 \times \frac{7}{6} - 4[/tex]
[tex] \frac{25}{6} = \frac{25}{6} [/tex]
Also,
[tex]| \frac{1}{8} + 3| = 7 \times \frac{1}{8} - 4[/tex]
[tex] \frac{25}{8} = - \frac{25}{8} [/tex]
This is an extraneous solution.
The only solution is:
[tex]x = \frac{7}{6} [/tex]
