Math  /  Algebra

QuestionThe equation 7(w3)=70-7(w-3)=70 is solved in several steps below. For each step, choose the reason that best justifies it. \begin{tabular}{|c|l|} \hline Step & Reason \\ \hline7(w3)=70-7(w-3)=70 & Given equation \\ \hline7(w3)7=707\frac{-7(w-3)}{-7}=\frac{70}{-7} & "Choose one" \\ \hlinew3=10w-3=-10 & "Choose one" \\ \hlinew3+3=10+3w-3+3=-10+3 & \begin{tabular}{l} Sddition Property of Equality \\ Subtraction Property of Equality \\ Multiplication Property of Equality \\ Division Property of Equality \\ Simplifying \end{tabular} \\ \hline & \begin{tabular}{l} Distributive Property \end{tabular} \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. We are solving the equation 7(w3)=70-7(w-3)=70.
2. Each step of the solution process requires a justification based on algebraic properties.
3. We need to identify the correct algebraic property for each step.

STEP 2

1. Justify the division step.
2. Justify the simplification step.
3. Justify the addition step.

STEP 3

The step 7(w3)7=707\frac{-7(w-3)}{-7}=\frac{70}{-7} involves dividing both sides of the equation by 7-7. This is justified by the:
Division Property of Equality
This property states that dividing both sides of an equation by the same non-zero number does not change the equality.

STEP 4

The step w3=10w-3=-10 is the result of simplifying the previous step. This is justified by:
Simplifying
This involves performing the division on both sides to reduce the equation to a simpler form.

STEP 5

The step w3+3=10+3w-3+3=-10+3 involves adding 33 to both sides of the equation. This is justified by the:
Addition Property of Equality
This property states that adding the same number to both sides of an equation does not change the equality.
The correct justifications for each step are: - Division Property of Equality - Simplifying - Addition Property of Equality

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