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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 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

3 answers

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
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

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 \(x=6\).