The solution is x = 11
Step-by-step explanation:
The original equation is
[tex]7(x+2)=91[/tex]
Lin uses the distributive property, which states that
[tex]a(x+y)=ax+ay[/tex]
By applying the property to this case,
[tex]7(x+2)=91\\7x+14=91[/tex]
Then we subtract 14 on both sides:
[tex]7x+14-14=91-14\\7x=77[/tex]
Finally, we divide by 7 on both sides:
[tex]\frac{7x}{7}=\frac{77}{7}\\x=11[/tex]
Noah starts by dividing each side by 7, so he gets
[tex]\frac{7(x+2)}{7}=\frac{91}{7}\\x+2=13[/tex]
Then he can subtract +2 from both sides:
[tex]x+2-2=13-2\\x=11[/tex]
So, they get the same result. The similarity between the two methods is that they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.
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Lin's solution method: 7x+14=91, 7x=77, x=11
Noah's solution method: x+2=13, x=11
Both methods involve dividing by 7, but Noah does the division first, while Lin does the division last. Also, Lin's method involves subtracting 14, while Noah's method involves subtracting 2. Both solutions are correct and valid. Noah's solution could be considered more efficient for this example, because it takes fewer steps and has equally complicated arithmetic work.
