A student solves the following equation for all possible values of x:
2 answers:
Given 
Then the solution follows thus:
<span>Step 1: 8(x – 4) = 2(x + 2)
Step 2: 4(x – 4) = (x + 2)
Step 3: 4x – 16 = x + 2
Step 4: 3x = 18
Step 5: x = 6</span>
It can be seen that his solution is correct. But 6 is not an extraneous solution.
<span>
An extraneous solution is a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the original problem.</span>
When 6 is substituted into the original equation, the original equation holds.
Therefore, h<span>is solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.</span>
Then the solution follows thus:
<span>Step 1: 8(x – 4) = 2(x + 2)
Step 2: 4(x – 4) = (x + 2)
Step 3: 4x – 16 = x + 2
Step 4: 3x = 18
Step 5: x = 6</span>
It can be seen that his solution is correct. But 6 is not an extraneous solution.
<span>
An extraneous solution is a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the original problem.</span>
When 6 is substituted into the original equation, the original equation holds.
Therefore, h<span>is solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.</span>
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