Math / Algebra

QuestionMoira solved a problem on the board. What error did Moira make and how can she correct it? $\begin{aligned} 12 x+10 & =54-10 x \\ 12 x+10-10 & =54-10 x-10 \\ 12 x & =44-10 x \\ 12 x-10 x & =44-10 x+10 x \\ 2 x & =44 \\ x & =22 \end{aligned}$ 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 $10 x$ , and on the right side of the equation, Moira should have subtracted $10 x$ . 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 $10 x$ , and on the right side of the equation, Moira should have also subtracted $10 x$ .

Studdy Solution

STEP 1

1. Moira is solving a linear equation for $x$ .
2. The goal is to isolate $x$ on one side of the equation.
3. We need to identify any algebraic errors in Moira's solution process.

STEP 2

1. Review Moira's solution step-by-step.
2. Identify the error in the algebraic manipulation.
3. Determine the correct algebraic operation.
4. Provide the corrected solution.

STEP 3

Review Moira's solution step-by-step:
1. Start with the original equation: $12x + 10 = 54 - 10x$ .
2. Subtract 10 from both sides: $12x + 10 - 10 = 54 - 10x - 10$ .
3. Simplify to: $12x = 44 - 10x$ .
4. Add $10x$ to both sides: $12x - 10x = 44 - 10x + 10x$ .
5. Simplify to: $2x = 44$ .
6. Solve for $x$ : $x = 22$ .

STEP 4

Identify the error in the algebraic manipulation:
Moira's error occurs in step 4. She incorrectly added $10x$ to both sides. Instead, she should have added $10x$ to the left side and subtracted $10x$ from the right side to maintain the equality.

STEP 5

Determine the correct algebraic operation:
To correct the error, Moira should have:
- Added $10x$ to the left side: $12x + 10x$ . - Subtracted $10x$ from the right side: $44 - 10x - 10x$ .

STEP 6

Provide the corrected solution:
1. Start with the equation: $12x + 10 = 54 - 10x$ .
2. Subtract 10 from both sides: $12x = 44 - 10x$ .
3. Add $10x$ to both sides: $12x + 10x = 44$ .
4. Simplify to: $22x = 44$ .
5. Solve for $x$ : $x = \frac{44}{22} = 2$ .
The correct solution is $x = 2$ .
The error was in the manipulation of $x$ terms. Moira should have added $10x$ to the left side and subtracted $10x$ from the right side. The correct solution is $x = 2$ .

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Studdy Solution

STEP 1

1. Moira is solving a linear equation for $x$ .
2. The goal is to isolate $x$ on one side of the equation.
3. We need to identify any algebraic errors in Moira's solution process.

STEP 2

1. Review Moira's solution step-by-step.
2. Identify the error in the algebraic manipulation.
3. Determine the correct algebraic operation.
4. Provide the corrected solution.

STEP 3

STEP 4

Identify the error in the algebraic manipulation:
Moira's error occurs in step 4. She incorrectly added $10x$ to both sides. Instead, she should have added $10x$ to the left side and subtracted $10x$ from the right side to maintain the equality.

STEP 5

Determine the correct algebraic operation:
To correct the error, Moira should have:
- Added $10x$ to the left side: $12x + 10x$ . - Subtracted $10x$ from the right side: $44 - 10x - 10x$ .

STEP 6

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Studdy Solution

STEP 1

1. Moira is solving a linear equation for x x x.2. The goal is to isolate x x x on one side of the equation.3. We need to identify any algebraic errors in Moira's solution process.

STEP 2

1. Review Moira's solution step-by-step.2. Identify the error in the algebraic manipulation.3. Determine the correct algebraic operation.4. Provide the corrected solution.

STEP 3

STEP 4

Identify the error in the algebraic manipulation:Moira's error occurs in step 4. She incorrectly added 10x 10x 10x to both sides. Instead, she should have added 10x 10x 10x to the left side and subtracted 10x 10x 10x from the right side to maintain the equality.

STEP 5

Determine the correct algebraic operation:To correct the error, Moira should have:- Added 10x 10x 10x to the left side: 12x+10x 12x + 10x 12x+10x. - Subtracted 10x 10x 10x from the right side: 44−10x−10x 44 - 10x - 10x 44−10x−10x.

STEP 6

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Moira is solving a linear equation for $x$ .
2. The goal is to isolate $x$ on one side of the equation.
3. We need to identify any algebraic errors in Moira's solution process.

1. Review Moira's solution step-by-step.
2. Identify the error in the algebraic manipulation.
3. Determine the correct algebraic operation.
4. Provide the corrected solution.

Identify the error in the algebraic manipulation:
Moira's error occurs in step 4. She incorrectly added $10x$ to both sides. Instead, she should have added $10x$ to the left side and subtracted $10x$ from the right side to maintain the equality.

Determine the correct algebraic operation:
To correct the error, Moira should have:
- Added $10x$ to the left side: $12x + 10x$ . - Subtracted $10x$ from the right side: $44 - 10x - 10x$ .