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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.

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    $\begingroup$ I suppose that the second $-6$ is just some sort of typo :) $\endgroup$ – b00n heT Jun 30 '16 at 18:06
  • $\begingroup$ Sasha why, did you mess up my question? $\endgroup$ – William Zlacki Jun 30 '16 at 18:23
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It doesn't mean anything. It's just a typo probably.

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${3x + 7 = 11}$

$-(3x + 7) = 11$

$3x + 7 = -11$

$3x = -18$

$x = -6$

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