Answered

Given: [tex]\(3(x-5)=x+3\)[/tex]
Prove: [tex]\(x=9\)[/tex]

[tex]\[
\begin{array}{|c|c|}
\hline
\text{Statement} & \text{Reason} \\
\hline
1. \, 3(x-5) = x + 3 & \text{Given} \\
\hline
2. \, 3x - 15 = x + 3 & \text{Distributive Property} \\
\hline
3. \, 2x - 15 = 3 & \text{Subtraction Property of Equality} \\
\hline
4. \, 2x = 18 & \text{Addition Property of Equality} \\
\hline
5. \, x = 9 & \text{Division Property of Equality} \\
\hline
\end{array}
\][/tex]

Complete the proof. What belongs in blank 2? Choose your answer.



Answer :

GinnyAnswer
To prove [tex]\( x = 9 \)[/tex] given the equation [tex]\( 3(x - 5) = x + 3 \)[/tex], we need to fill in the missing statements in the provided proof table. Let's complete the proof step-by-step:

Given equation:
[tex]\[ 3(x - 5) = x + 3 \][/tex]

### Proof Table Completion

| Statement | Reason |
|----------------------|---------------------------------------------|
| 1. [tex]\( 3(x - 5) = x + 3 \)[/tex] | 1. Given |
| 2. [tex]\( 3x - 15 = x + 3 \)[/tex] | 2. Distributive Property of Equality |
| 3. [tex]\( 2x - 15 = 3 \)[/tex] | 3. Subtraction Property of Equality |
| 4. [tex]\( 2x = 18 \)[/tex] | 4. Addition Property of Equality |
| 5. [tex]\( x = 9 \)[/tex] | 5. Division Property of Equality |

### Step-by-Step Solution:

1. Given: [tex]\( 3(x - 5) = x + 3 \)[/tex].
_This is the equation we start with._

2. Distributive Property of Equality: Distribute the [tex]\( 3 \)[/tex] on the left side.
[tex]\[ 3(x - 5) = 3x - 15 \][/tex]
So, the equation [tex]\( 3(x - 5) = x + 3 \)[/tex] becomes:
[tex]\[ 3x - 15 = x + 3 \][/tex]

3. Subtraction Property of Equality: Subtract [tex]\( x \)[/tex] from both sides to move the [tex]\( x \)[/tex]-terms to one side.
[tex]\[ 3x - x - 15 = 3 \][/tex]
Simplifying the equation:
[tex]\[ 2x - 15 = 3 \][/tex]

4. Addition Property of Equality: Add 15 to both sides to isolate the [tex]\( x \)[/tex]-term.
[tex]\[ 2x - 15 + 15 = 3 + 15 \][/tex]
Simplifying the equation:
[tex]\[ 2x = 18 \][/tex]

5. Division Property of Equality: Divide both sides by 2 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{18}{2} \][/tex]
Simplifying the equation:
[tex]\[ x = 9 \][/tex]

Thus, your proof table is now complete, and the correct choice for blank 2 is:
[tex]\[ \boxed{3x - 15 = x + 3} \][/tex]

Other Questions