When solving the problem 6x^+3 = 6^2x-5, your friend does the following:
6(x) +3=2(2x)-5
6x+3=12x-5
8=6x
x =4/3
Was this correct?
Responses
Both sides should be divided by 6 instead of multiplied by 6.
Both sides should be divided by 6 instead of multiplied by 6.
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 6 needs to be distributed across all terms when solving.
The first response is correct. The mistake was in multiplying both sides by 6 instead of dividing by 6. The correct steps should be to first simplify the equation:
6x^+3 = 6^2x-5
6(x + 3) = 6^(2x-5)
x + 3 = 2x - 5
Now, we can solve for x:
x + 3 = 2x - 5
x - 2x = -5 - 3
-x = -8
x = 8
Therefore, the correct solution is x = 8.