# The double ${-6}$, from ${|3x + 7| = 11}$

Solve for $x$ such that $|3x + 7| = 11$.

Answer. "${x = \frac {4}{3}, -6, -6}$". First rewrite the absolute value equation as two separate linear equations. In the first equation, assume that the ${3 + 7}$ is positive and set it equal to 11. In the second equation, also equal to 11, assume that the ${(3x + 7)}$ is negative. For that one, negate (multiply by -1) the whole binomial, and then solve the equation.

${3x + 7 = 11}$

${3x = 4}$

${x = \frac {4}{3}}$

$-(3x + 7) = 11$

${-3x - 7 = 11}$

$-3x = 18$

${x = -6}$

Where does a double -6 apply.

• I suppose that the second $-6$ is just some sort of typo :) – b00n heT Jun 30 '16 at 18:06
• Sasha why, did you mess up my question? – William Zlacki Jun 30 '16 at 18:23

${3x + 7 = 11}$
$-(3x + 7) = 11$
$3x + 7 = -11$
$3x = -18$
$x = -6$