How do you solve $4 d + 7 = - | 2 d + 41 |$ $4d + 7 = - abs(2d + 41)$ ?

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Answer 1 · 2018-07-26T18:57:46

$d = - 8$ $d=-8$

Given that

$4 d + 7 = - | 2 d + 41 |$ $4d+7=-|2d+41|$

Case 1: When $2d+41\ge 0\ \ or \ \ d\ge -41/2$

$4d+7=-(2d+41)$

$4d+7=-2d-41$

$6d=-48$

$d=-48/6$

$d=-8$

Since $d=-8> -41/2$ hence $d=-8$ is a solution

Case 2: When $2d+41<0\ \ or \ \ d< -41/2$

$4d+7=-(-(2d+41))$

$4d+7=2d+41$

$2d=34$

$d=17$

But $d< -41/2$ hence $d=17$ is not a solution

Hence, the only solution to the given equation is

$d=-8$

How do you solve 4d + 7 = - abs(2d + 41) 4d+7=−|2d+41|4d + 7 = - abs(2d + 41) ?