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Fill in the missing justifications in the correct order.

[tex]\[
\begin{tabular}{|l|l|}
\hline Mathematical Statement & \multicolumn{1}{|c|}{ Justification } \\
\hline $4x + 3 = x + 5 - 2x$ & Given \\
\hline $4x + 3 = x - 2x + 5$ & Commutative Property of Addition \\
\hline $4x + 3 = -x + 5$ & Combine Like Terms \\
\hline $5x + 3 = 5$ & Addition Property of Equality \\
\hline $5x = 2$ & Subtraction Property of Equality \\
\hline $x = \frac{2}{5}$ & Division Property of Equality \\
\hline
\end{tabular}
\][/tex]

Options:
A. Combine Like Terms; Subtraction Property of Equality; Addition Property of Equality; Division Property of Equality
B. Combine Like Terms; Addition Property of Equality; Subtraction Property of Equality; Division Property of Equality
C. Addition Property of Equality; Combine Like Terms; Subtraction Property of Equality; Division Property of Equality
D. Subtraction Property of Equality; Division Property of Equality; Addition Property of Equality; Combine Like Terms

Correct Answer:
B. Combine Like Terms; Addition Property of Equality; Subtraction Property of Equality; Division Property of Equality

Sagot :

GinnyAnswer
Let's fill in the missing justifications step-by-step in the correct order.

Given statement:
[tex]\[ 4x + 3 = x + 5 - 2x \][/tex]

### First Step:
[tex]\[ 4x + 3 = x - 2x + 5 \][/tex]
Justification: Commutative Property of Addition (rearranging terms on the right side)

### Second Step:
[tex]\[ 4x + 3 = -x + 5 \][/tex]
Justification: Combine Like Terms (combining [tex]\( x \)[/tex] and [tex]\( -2x \)[/tex])

### Third Step:
[tex]\[ 5x + 3 = 5 \][/tex]
Justification: Addition Property of Equality (adding [tex]\( x \)[/tex] to both sides)

### Fourth Step:
[tex]\[ 5x = 2 \][/tex]
Justification: Subtraction Property of Equality (subtracting 3 from both sides)

### Fifth Step:
[tex]\[ x = \frac{2}{5} \][/tex]
Justification: Division Property of Equality (dividing both sides by 5)

So the complete table with justifications should look like this:

[tex]\[ \begin{tabular}{|l|l|} \hline Mathematical Statement & \multicolumn{1}{c|}{Justification} \\ \hline $4 x + 3 = x + 5 - 2 x$ & Given \\ \hline $4 x + 3 = x - 2 x + 5$ & Commutative Property of Addition \\ \hline $4 x + 3 = - x + 5$ & Combine Like Terms \\ \hline $5 x + 3 = 5$ & Addition Property of Equality \\ \hline $5 x = 2$ & Subtraction Property of Equality \\ \hline $x = \frac{2}{5}$ & Division Property of Equality \\ \hline \end{tabular} \][/tex]

The correct order for the justifications is:
1. Commutative Property of Addition
2. Combine Like Terms
3. Addition Property of Equality
4. Subtraction Property of Equality
5. Division Property of Equality
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