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

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Answer 1 · 2018-07-26T18:57:46

#d=-8#

Given that

#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#