How do you solve $| 9 n + 8 | = 46$ $abs(9n+8)=46$ ?

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Answer 1 · 2016-10-03T14:20:07

$x = (4.2, - 5.88)$ $x=(4.2,-5.88)$

$| 9 n + 8 | = 46$ $color(blue)(|9n+8|=46$

First of all, the equation is in absolute value

So we can make it into two equations

$9 n + 8 = 46$ $color(orange)(9n+8=46$

$9 n + 8 = - 46$ $color(violet)(9n+8=-46$

Solve for the equations

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$\to 9 n + 8 = 46$ $rarrcolor(orange)(9n+8=46$

$\to 9 n = 46 - 8$ $rarrcolor(orange)(9n=46-8$

$\to 9 n = 38$ $rarrcolor(orange)(9n=38$

$\to n = \frac{38}{9} = 4.2$ $rarrcolor(green)(n=38/9=4.2$

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$\to 9 n + 8 = - 46$ $rarrcolor(violet)(9n+8=-46$

$\to 9 n = - 46 - 8$ $rarrcolor(violet)(9n=-46-8$

$\to 9 n = - 53$ $rarrcolor(violet)(9n=-53$

$\to n = - \frac{53}{9} = - 5.88$ $rarrcolor(green)(n=-53/9=-5.88$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$:.color(green)(x=(4.2,-5.88)$

How do you solve abs(9n+8)=46|9n+8|=46abs(9n+8)=46?