Answer:
No, Gloria is not correct. The solution for the first expression "-6x + 6", is not equivalent to the second expression's solution "-6x - 6".
Step-by-step explanation:
[tex]\dfrac{ 1 }{ 4 } \left( 12x+24 \right)-9x[/tex]
Use the distributive property to multiply [tex]\frac{1}{4}[/tex] by 12x + 24
[tex]\dfrac{ 1 }{ 4 } \times 12x+ \dfrac{ 1 }{ 4 } \times 24-9x[/tex]
Multiply [tex]\frac{1}{4}[/tex] and 12 to get [tex]\frac{12}{4}[/tex]
[tex]\dfrac{ 12 }{ 4 } x+ \dfrac{ 1 }{ 4 } \times 24-9x[/tex]
Divide 12 by 4 to get 3
[tex]3x+ \dfrac{ 1 }{ 4 } \times 24-9x[/tex]
Multiply [tex]\frac{1}{4}[/tex] and 24 to get [tex]\frac{24}{4}[/tex]
[tex]3x+ \dfrac{ 24 }{ 4 } -9x[/tex]
Divide 24 by 4 to get 6
[tex]3x + 6-9x[/tex]
Combine 3x and -9x to get -6x
-6x + 6
So the answer for the first expression is -6x + 6
Now lets solve the second expression
-6 ( x + 1)
Use the distributive property to multiply −6 by x + 1
-6x - 6
So the answer for the second expression is -6x - 6
So we can conclude that the two expressions are not equivalent
