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Question
Mathematics
In the problem below, which line contains an error?
Line 1: 6 x 2 ( x 5 ) = 20 6x-2(x-5)=20
Line 2: 6 x 2 x + 10 = 20 6x-2x+10=20
Line 3: 4 x + 10 = 20 4x+10=20
Line 4 : x + 10 = 5 4:x+10=5
Line 5: x = 2 x=2
Line 2
Line 3
Line 4
Line 5
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Best Answer
The error is in Line 4.
The equations before line 4 are correct simplifications of the original equation.
6 x 2 ( x 5 ) = 20 6x-2(x-5)=20
6 x 2 x + 10 = 20 6x-2x+10=20
4 x + 10 = 20 4x+10=20
However, to isolate x x, we need to subtract 10 10 from both sides of the equation, not add 10 10:
4 x + 10 10 = 20 10 4x+10-10=20-10
4 x = 10 4x=10
Dividing both sides by 4 4, we get:
x = 10 4 = 2 x=(10)/(4)=2
Therefore, the correct line 4 should be:
4 x = 10 4x=10
The error is that 10 10 was mistakenly added instead of subtracted from both sides of the equation in line 4.
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