How do you solve $| - 3 (x - 7) | = 21$ $|- 3( x - 7) | = 21$ ?

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Answer 1 · 2018-04-12T01:49:17

$x = 0$ $x = 0$ and $x = 14$ $x = 14$

Because $| 21 | = | - 21 | = 21$ $|21| = |-21| = 21$ , we can remove the absolute value from the equation as such

$| - 3 (x - 7) | = 21$ $|-3(x-7)| = 21$
$- 3 (x - 7) = \pm 21$ $-3(x-7) = +- 21$

We then have two equations (differentiated by the $\pm$ $+-$ sign) and we solve each using equation manipulation.

$- 3 (x - 7) = 21$ $-3(x-7) = 21$
$21 - 3 x = 21$ $21 - 3x = 21$
$3 x = 0 \to x = 0$ $3x = 0 -> x = 0$

$- 3 (x - 7) = - 21$ $-3(x-7) = -21$
$21 - 3 x = - 21$ $21 - 3x = -21$
$42 = 3 x$ $42 = 3x$
$x = \frac{42}{3} = 14$ $x = 42/3 = 14$

Thus, our two solutions are $x = 0$ $x = 0$ and $x = 14$ $x = 14$ .

How do you solve |−3(x−7)|=21|- 3( x - 7) | = 21?