When solving the problem 7x+2=73x−8
, your friend does the following:
7(x)+2=7(3x)−8
7x+2=21x−8
10=14x
x=57
Was this correct?
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Responses
When the bases are the same, then we can set the exponents equal to each other and solve that equation.
When the bases are the same, then we can set the exponents equal to each other and solve that equation.
Yes, this is correct. No error was made.
Yes, this is correct. No error was made.
The 7 needs to be distributed across all terms when solving.
The 7 needs to be distributed across all terms when solving.
Both sides should be divided by 7 instead of multiplied by 7.
Both sides should be divided by 7 instead of multiplied by 7.
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No, this is not correct. Your friend distributed the 7 only on the left side of the equation, but not on the right side. To solve the equation correctly, you need to distribute the 7 on both sides:
7(x) + 2 = 7(3x) - 8
7x + 2 = 21x - 8
Then, you can combine like terms:
7x + 2 = 21x - 8
-14x + 2 = -8
From there, you can isolate the variable by subtracting 2 from both sides:
-14x + 2 - 2 = -8 - 2
-14x = -10
Finally, divide both sides by -14 to solve for x:
-14x / -14 = -10 / -14
x = 10/14
x = 5/7
So the correct solution is x = 5/7.