Math  /  Algebra

QuestionMoira solved a problem on the board. What error did Moira make and how can she correct it? 12x+10=5410x12x+1010=5410x1012x=4410x12x10x=4410x+10x2x=44x=22\begin{aligned} 12 x+10 & =54-10 x \\ 12 x+10-10 & =54-10 x-10 \\ 12 x & =44-10 x \\ 12 x-10 x & =44-10 x+10 x \\ 2 x & =44 \\ x & =22 \end{aligned} On the left side of the equation, Moira should have subtracted 10x and on the right side of the equation, Moira should have added 10x. On the left side of the equation, Moira should have added 10x10 x, and on the right side of the equation, Moira should have subtracted 10x10 x. On the left side of the equation, Moira should have added 10x, and on the right side of the equation, Moira should have also added 10x. On the left side of the equation, Moira should have subtracted 10x10 x, and on the right side of the equation, Moira should have also subtracted 10x10 x.

Studdy Solution
Provide the corrected solution:
1. Start with the equation: 12x+10=5410x 12x + 10 = 54 - 10x .
2. Subtract 10 from both sides: 12x=4410x 12x = 44 - 10x .
3. Add 10x 10x to both sides: 12x+10x=44 12x + 10x = 44 .
4. Simplify to: 22x=44 22x = 44 .
5. Solve for x x : x=4422=2 x = \frac{44}{22} = 2 .

The correct solution is x=2 x = 2 .
The error was in the manipulation of x x terms. Moira should have added 10x 10x to the left side and subtracted 10x 10x from the right side. The correct solution is x=2 x = 2 .

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