Question

9 given: 10k - 4 = 2k - 20; prove: k = -2
statements\treasons

Explanation:

Step1: Subtract \(2k\) from both sides

To isolate the variable terms on one side, we subtract \(2k\) from each side of the equation \(10k - 4 = 2k - 20\). This gives us \(10k - 2k - 4 = 2k - 2k - 20\), which simplifies to \(8k - 4 = -20\). The reason for this step is the Subtraction Property of Equality (if \(a = b\), then \(a - c = b - c\)).

Step2: Add 4 to both sides

Next, we add 4 to both sides of the equation \(8k - 4 = -20\) to isolate the term with the variable. So, \(8k - 4 + 4 = -20 + 4\), which simplifies to \(8k = -16\). The reason here is the Addition Property of Equality (if \(a = b\), then \(a + c = b + c\)).

Step3: Divide both sides by 8

Finally, we divide both sides of the equation \(8k = -16\) by 8 to solve for \(k\). This gives us \(\frac{8k}{8}=\frac{-16}{8}\), which simplifies to \(k = -2\). The reason for this step is the Division Property of Equality (if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)).

Filling in the table:

Statements	Reasons
\(8k - 4 = -20\)	Subtraction Property of Equality (subtract \(2k\) from both sides)
\(8k = -16\)	Addition Property of Equality (add 4 to both sides)
\(k = -2\)	Division Property of Equality (divide both sides by 8)

Answer:

The proof is completed as shown in the table above, and we have proven that \(k = -2\).