Question

question
choose the justification for each step in the solution to the given equation.

step	statement	reason
2	\\(-2x - 7 = -15\\)	\\(\boldsymbol{\

abla}\\) |

3

\\(-2x - 7 + 7 = -15 + 7\\)

\\(\boldsymbol{\

abla}\\) |

4

\\(-2x = -8\\)

\\(\boldsymbol{\

abla}\\) |

5

\\(\frac{-2x}{-2} = \frac{-8}{-2}\\)

\\(\boldsymbol{\

abla}\\) |

6

\\(x = 4\\)

\\(\boldsymbol{\

abla}\\) (dropdown with options: addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality, simplification) |

Explanation:

Step 2:

Step1: Identify the operation.

We have \(\frac{1}{4}x - \frac{9}{4}x\). Combining like terms: \(\frac{1 - 9}{4}x=\frac{-8}{4}x = - 2x\). So the reason is simplification.

Step2: For step 3.

We add 7 to both sides of \(-2x - 7=-15\) to get \(-2x - 7 + 7=-15 + 7\). This is the addition property of equality (adding the same number to both sides of an equation).

Step3: For step 4.

Simplify \(-2x - 7 + 7\) to \(-2x\) and \(-15 + 7\) to \(-8\). So the reason is simplification.

Step4: For step 5.

We divide both sides of \(-2x=-8\) by \(-2\) to get \(\frac{-2x}{-2}=\frac{-8}{-2}\). This is the division property of equality (dividing both sides of an equation by the same non - zero number).

Step5: For step 6.

Simplify \(\frac{-2x}{-2}\) to \(x\) and \(\frac{-8}{-2}\) to \(4\). So the reason is simplification.

Step - by - Step Justification:

• Step 2 Reason: Simplification (combining like terms \(\frac{1}{4}x-\frac{9}{4}x=-2x\))
• Step 3 Reason: Addition property of equality (adding 7 to both sides)
• Step 4 Reason: Simplification (simplifying \(-2x - 7+7\) and \(-15 + 7\))
• Step 5 Reason: Division property of equality (dividing both sides by \(-2\))
• Step 6 Reason: Simplification (simplifying \(\frac{-2x}{-2}\) and \(\frac{-8}{-2}\))

Final Answers for Each Step:

• Step 2: simplification
• Step 3: addition property of equality
• Step 4: simplification
• Step 5: division property of equality
• Step 6: simplification

Answer:

Step1: Identify the operation.

We have \(\frac{1}{4}x - \frac{9}{4}x\). Combining like terms: \(\frac{1 - 9}{4}x=\frac{-8}{4}x = - 2x\). So the reason is simplification.

Step2: For step 3.

We add 7 to both sides of \(-2x - 7=-15\) to get \(-2x - 7 + 7=-15 + 7\). This is the addition property of equality (adding the same number to both sides of an equation).

Step3: For step 4.

Simplify \(-2x - 7 + 7\) to \(-2x\) and \(-15 + 7\) to \(-8\). So the reason is simplification.

Step4: For step 5.

We divide both sides of \(-2x=-8\) by \(-2\) to get \(\frac{-2x}{-2}=\frac{-8}{-2}\). This is the division property of equality (dividing both sides of an equation by the same non - zero number).

Step5: For step 6.

Simplify \(\frac{-2x}{-2}\) to \(x\) and \(\frac{-8}{-2}\) to \(4\). So the reason is simplification.

Step - by - Step Justification:

• Step 2 Reason: Simplification (combining like terms \(\frac{1}{4}x-\frac{9}{4}x=-2x\))
• Step 3 Reason: Addition property of equality (adding 7 to both sides)
• Step 4 Reason: Simplification (simplifying \(-2x - 7+7\) and \(-15 + 7\))
• Step 5 Reason: Division property of equality (dividing both sides by \(-2\))
• Step 6 Reason: Simplification (simplifying \(\frac{-2x}{-2}\) and \(\frac{-8}{-2}\))

Final Answers for Each Step:

• Step 2: simplification
• Step 3: addition property of equality
• Step 4: simplification
• Step 5: division property of equality
• Step 6: simplification