Question

drag each step and justification to the correct location on the table. each step and justification can be used more than once, but not all steps and justifications will be used. order each step and justification that is needed to solve the equation below. -2x = 28 - 6x | steps | justifications | | --- | --- | | -2x = 28 - 6x | given | | -2x + 6x = 28 - 6x + 6x | | | | simplification | | | | | | simplification | -4x = 28 4x/4 = 28/4 4x = 28 x = 7 addition property of equality (-4x)/(-4) = 28/(-4) x = -7 division property of equality

Explanation:

Step1: Identify the justification for the second step

The step \(-2x + 6x = 28 - 6x + 6x\) is obtained by adding \(6x\) to both sides of the equation \(-2x = 28 - 6x\). This is justified by the Addition property of equality.

Step2: Simplify the second step

Simplify \(-2x + 6x = 28 - 6x + 6x\). Combining like terms, we get \(4x=28\). This step is justified by Simplification.

Step3: Apply division property of equality

To solve for \(x\), we divide both sides of the equation \(4x = 28\) by \(4\). So we have \(\frac{4x}{4}=\frac{28}{4}\). This is justified by the Division property of equality.

Step4: Simplify the last step

Simplify \(\frac{4x}{4}=\frac{28}{4}\) to get \(x = 7\). This step is justified by Simplification.

Now, filling the table:

Steps	Justifications
\(-2x + 6x = 28 - 6x + 6x\)	Addition property of equality
\(4x = 28\)	Simplification
\(\frac{4x}{4}=\frac{28}{4}\)	Division property of equality
\(x = 7\)	Simplification

Answer:

The completed table with steps and justifications is as follows:

Steps	Justifications
\(-2x + 6x = 28 - 6x + 6x\)	Addition property of equality
\(4x = 28\)	Simplification
\(\frac{4x}{4}=\frac{28}{4}\)	Division property of equality
\(x = 7\)	Simplification

(If we consider the blanks in the original table, the steps and justifications to fill are:

• For the second row (step \(-2x + 6x = 28 - 6x + 6x\)): Justification is "Addition property of equality"
• For the third row (step \(4x = 28\)): Justification is "Simplification"
• For the fourth row (step \(\frac{4x}{4}=\frac{28}{4}\)): Justification is "Division property of equality"
• For the fifth row (step \(x = 7\)): Justification is "Simplification")