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A student solved an equation, as shown below. The first line shows 1 over 4 left Parenthesis 8 minus 12x right parenthesis equa...Asked by AYD3N
A student solved an equation, as shown below.
The first line shows 1 over 4 left Parenthesis 8 minus 12x right parenthesis equals x minus 2 left parenthesis 2x plus 1 right parenthesis, second line shows 2 minus 3x equals x minus 4x plus 2, third line shows 2 minus 3x equals 3x plus 2, fourth line shows 2 minus 3x plus 3x equals negative 3x plus 3x plus 2. Fifth line shows 2 equals 2.
Based on the student's work, complete the statement below.
Use the drop-down menus to make the statement below true.
The student solved the equation Query 1 options: correct, incorrect
because the original equation has Query 2 options: no solutions, one solution, infinite solutions
The first line shows 1 over 4 left Parenthesis 8 minus 12x right parenthesis equals x minus 2 left parenthesis 2x plus 1 right parenthesis, second line shows 2 minus 3x equals x minus 4x plus 2, third line shows 2 minus 3x equals 3x plus 2, fourth line shows 2 minus 3x plus 3x equals negative 3x plus 3x plus 2. Fifth line shows 2 equals 2.
Based on the student's work, complete the statement below.
Use the drop-down menus to make the statement below true.
The student solved the equation Query 1 options: correct, incorrect
because the original equation has Query 2 options: no solutions, one solution, infinite solutions
Answers
Answered by
AYD3N
Jackson solved the problem 3x-8=2(2x-7) using the following steps:
STEP 1: Use Distributive Property to get 3x-8=4x-14
STEP 2: Use Addition Property of Equality to get 3x = 4x-14+8
STEP 3: Combine Like Terms to get 3x = 4x-6
STEP 4: Use Subtraction Property of Equality to get 3x-4x= -6
STEP 5: Combine Like Terms to get (-x)=-6
What is the last step?
A.
Use Property of Equality to get x= (-6)
B.
Divide both sides by -1 to get x=6
C.
Divide both sides by -1 to get x= (-6)
D.
Use Multiplication Property of Equality to get x=6
STEP 1: Use Distributive Property to get 3x-8=4x-14
STEP 2: Use Addition Property of Equality to get 3x = 4x-14+8
STEP 3: Combine Like Terms to get 3x = 4x-6
STEP 4: Use Subtraction Property of Equality to get 3x-4x= -6
STEP 5: Combine Like Terms to get (-x)=-6
What is the last step?
A.
Use Property of Equality to get x= (-6)
B.
Divide both sides by -1 to get x=6
C.
Divide both sides by -1 to get x= (-6)
D.
Use Multiplication Property of Equality to get x=6
Answered by
GPT-4o mini
To analyze the student's solution, let's first break down the steps mentioned in the lines provided:
1. The first line:
\[
\frac{1}{4}(8 - 12x) = x - 2(2x + 1)
\]
This can be simplified as:
\[
\frac{1}{4}(8 - 12x) = x - 4x - 2 \Rightarrow \frac{1}{4}(8 - 12x) = -3x - 2
\]
2. The second line:
The student simplified the equation to:
\[
2 - 3x = -3x - 2
\]
3. The third line:
This step seems incorrect because it looks like \(2 - 3x = x - 4x + 2\) should lead to:
\[
2 - 3x = -3x + 2
\]
However, both sides are equal if simplified correctly.
4. The student's fourth line states:
\[
2 - 3x + 3x = -3x + 3x + 2
\]
This simplifies to:
\[
2 = 2
\]
Expectedly, if the two sides are equal, this situation indicates that the original equation is satisfied for all \(x\), meaning it has infinite solutions.
Therefore, we conclude:
The student solved the equation **correct** because the original equation has **infinite solutions**.
Final selection:
- **Correct**
- **Infinite solutions**
1. The first line:
\[
\frac{1}{4}(8 - 12x) = x - 2(2x + 1)
\]
This can be simplified as:
\[
\frac{1}{4}(8 - 12x) = x - 4x - 2 \Rightarrow \frac{1}{4}(8 - 12x) = -3x - 2
\]
2. The second line:
The student simplified the equation to:
\[
2 - 3x = -3x - 2
\]
3. The third line:
This step seems incorrect because it looks like \(2 - 3x = x - 4x + 2\) should lead to:
\[
2 - 3x = -3x + 2
\]
However, both sides are equal if simplified correctly.
4. The student's fourth line states:
\[
2 - 3x + 3x = -3x + 3x + 2
\]
This simplifies to:
\[
2 = 2
\]
Expectedly, if the two sides are equal, this situation indicates that the original equation is satisfied for all \(x\), meaning it has infinite solutions.
Therefore, we conclude:
The student solved the equation **correct** because the original equation has **infinite solutions**.
Final selection:
- **Correct**
- **Infinite solutions**
Answered by
GPT-4o mini
To find the last step in Jackson's solution to the equation \(3x - 8 = 2(2x - 7)\), let's summarize the steps leading to STEP 5:
1. The original equation is \(3x - 8 = 4x - 14\).
2. After using properties of equality and combining like terms, we reached STEP 5:
\[
(-x) = -6.
\]
Now, to solve for \(x\), we need to isolate \(x\) by dividing both sides by \(-1\):
\[
x = -(-6) = 6.
\]
So the correct final step is:
**B. Divide both sides by -1 to get \(x=6\).**
1. The original equation is \(3x - 8 = 4x - 14\).
2. After using properties of equality and combining like terms, we reached STEP 5:
\[
(-x) = -6.
\]
Now, to solve for \(x\), we need to isolate \(x\) by dividing both sides by \(-1\):
\[
x = -(-6) = 6.
\]
So the correct final step is:
**B. Divide both sides by -1 to get \(x=6\).**
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