Respuesta :
The correct answer is: [B]: " m = -12 " .
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Explanation:
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Given the equation:
→ " ³√(m − 4) − ³√(2m + 8) = 0 " ; Solve for "m" ;
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We start by rewriting the terms in the equation:
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Note the following property of exponents:
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→ " a ⁽ ˣ / ʸ⁾ = ʸ√(aˣ) ; { y [tex]\neq [/tex] 0 } " ;
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So, rewrite: " ³√(m − 4) " ; as: " (m − 4) ⁽ ¹/³⁾ " ;
and rewrite: " ³√(2m + 8) " ; as: " (2m + 8) ⁽ ¹/³⁾ " ;
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And rewrite the question as:
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→ " (m − 4) ⁽ ¹/³⁾ − (2m + 8) ⁽ ¹/³⁾ = 0 " ; Solve for "m" ;
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Add " (2m + 8) ¹/³ " to EACH SIDE of the equation; as follows:
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→ (m − 4) ¹/³⁾ − (2m + 8)¹/³ + (2m + 8) ¹/³ = 0 + (2m + 8) ¹/³ ;
to get:
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→ " (m − 4) ¹/³ = (2m + 8) ¹/³ " ;
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→ { Note: If " x ⁿ = y ⁿ ; then " x = y " .} .
_________________________________________________________ As such:
→ " m − 4 = 2m + 8 " ; Solve for "m" ;
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Subtract "2m" from each side of the equation; & add "4" to each side of the equation; as follows:
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m − 4 − 2m + 4 = 2m + 8 − 2m + 4 ;
to get:
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→ -1m = 12 ;
Now, divide each side of the equation by "-1 " ;
to isolation "m" on one side of the equation; & to solve for "m" ;
→ -1m / -1 = 12 / -1 ;
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to get:
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" m = -12 " ;
→ which is: Answer choice: [B]: " m = -12 " .
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Hope this helps!
Best wishes.
_________________________________________________________
________________________________________________________
Explanation:
_________________________________________________________
Given the equation:
→ " ³√(m − 4) − ³√(2m + 8) = 0 " ; Solve for "m" ;
_________________________________________________________
We start by rewriting the terms in the equation:
_________________________________________________________
Note the following property of exponents:
_________________________________________________________
→ " a ⁽ ˣ / ʸ⁾ = ʸ√(aˣ) ; { y [tex]\neq [/tex] 0 } " ;
_________________________________________________________
So, rewrite: " ³√(m − 4) " ; as: " (m − 4) ⁽ ¹/³⁾ " ;
and rewrite: " ³√(2m + 8) " ; as: " (2m + 8) ⁽ ¹/³⁾ " ;
_________________________________________________________
And rewrite the question as:
_________________________________________________________
→ " (m − 4) ⁽ ¹/³⁾ − (2m + 8) ⁽ ¹/³⁾ = 0 " ; Solve for "m" ;
_________________________________________________________
Add " (2m + 8) ¹/³ " to EACH SIDE of the equation; as follows:
_________________________________________________________
→ (m − 4) ¹/³⁾ − (2m + 8)¹/³ + (2m + 8) ¹/³ = 0 + (2m + 8) ¹/³ ;
to get:
_________________________________________________________
→ " (m − 4) ¹/³ = (2m + 8) ¹/³ " ;
_________________________________________________________
→ { Note: If " x ⁿ = y ⁿ ; then " x = y " .} .
_________________________________________________________ As such:
→ " m − 4 = 2m + 8 " ; Solve for "m" ;
_________________________________________________________
Subtract "2m" from each side of the equation; & add "4" to each side of the equation; as follows:
_________________________________________________________
m − 4 − 2m + 4 = 2m + 8 − 2m + 4 ;
to get:
_________________________________________________________
→ -1m = 12 ;
Now, divide each side of the equation by "-1 " ;
to isolation "m" on one side of the equation; & to solve for "m" ;
→ -1m / -1 = 12 / -1 ;
_________________________________________________________
to get:
_________________________________________________________
" m = -12 " ;
→ which is: Answer choice: [B]: " m = -12 " .
_________________________________________________________
Hope this helps!
Best wishes.
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