Let's complete the missing reasons step by step.
Given equation: [tex]\( 4(x - 2) = 6x + 18 \)[/tex]
[tex]\[
\begin{array}{|l|l|}
\hline
\text{Statements} & \text{Reasons} \\
\hline
1. \ 4(x - 2) = 6x + 18 & \text{Given} \\
\hline
2. \ 4x - 8 = 6x + 18 & \text{Distributive property} \\
\hline
3. \ -2x - 8 = 18 & \text{Subtraction property of equality} \\
\hline
4. \ -2x = 26 & \text{Addition property of equality} \\
\hline
5. \ x = -13 & \text{Division property of equality} \\
\hline
\end{array}
\][/tex]
By following the steps:
- Step 1 (Given): [tex]\( 4(x - 2) = 6x + 18 \)[/tex]
- Step 2 (Distributive property applied): [tex]\( 4(x - 2) \rightarrow 4x - 8 \)[/tex], thus equation becomes [tex]\( 4x - 8 = 6x + 18 \)[/tex]
- Step 3 (Subtraction property of equality): Subtract [tex]\( 6x \)[/tex] from both sides gives [tex]\( 4x - 6x - 8 = 18 \)[/tex] which simplifies to [tex]\( -2x - 8 = 18 \)[/tex]
- Step 4 (Addition property of equality): Add [tex]\( 8 \)[/tex] to both sides to isolate [tex]\( x \)[/tex]-term: [tex]\( -2x - 8 + 8 = 18 + 8 \)[/tex], simplifying to [tex]\( -2x = 26 \)[/tex]
- Step 5 (Division property of equality): Divide both sides by [tex]\( -2 \)[/tex] to solve for [tex]\( x \)[/tex]: [tex]\( \frac{-2x}{-2} = \frac{26}{-2} \)[/tex], simplifying to [tex]\( x = -13 \)[/tex]
Thus, the correct reasons are:
- Step 3: Subtraction property of equality
- Step 5: Division property of equality
So, the correct completion of the missing reasons is the option:
3. subtraction property of equality; 5. division property of equality
