College

Drag a statement or reason to each box to complete the proof.

If [tex]7(x-2) = x + 16[/tex], then [tex]x = 5[/tex].

**Statement**
1. [tex]7(x-2) = x + 16[/tex]
2. [tex]7x - 14 = x + 16[/tex]
3. [tex]7x - 14 + 14 = x + 16 + 14[/tex]
4. [tex]7x = x + 30[/tex]
5. [tex]7x - x = x + 30 - x[/tex]

Answer :

Sure! Let's go through the steps to solve the equation [tex]\(7(x-2) = x + 16\)[/tex] and prove that [tex]\(x = 5\)[/tex].

### Step-by-Step Solution

Statement 1: [tex]\( 7(x - 2) = x + 16 \)[/tex]

This is the given equation we want to solve.

Statement 2: [tex]\( 7x - 14 = x + 16 \)[/tex]

Reason: Distribute the 7 to both terms inside the parenthesis.

When distributing, we get:
[tex]\[ 7(x - 2) = 7x - 14 \][/tex]

Statement 3: [tex]\( 7x - 14 + 14 = x + 16 + 14 \)[/tex]

Reason: Add 14 to both sides to simplify.

To isolate the term with [tex]\(x\)[/tex], we add 14 to both sides:
[tex]\[ 7x - 14 + 14 = x + 16 + 14 \][/tex]
[tex]\[ 7x = x + 30 \][/tex]

Statement 4: [tex]\( 7x - x = x + 30 - x \)[/tex]

Reason: Subtract [tex]\(x\)[/tex] from both sides to consolidate the [tex]\(x\)[/tex] terms on one side.

Subtract [tex]\(x\)[/tex] from both sides to get:
[tex]\[ 7x - x = x + 30 - x \][/tex]
[tex]\[ 6x = 30 \][/tex]

Statement 5: [tex]\( 6x = 30 \)[/tex]

Reason: Simplify the expression after subtraction.

Now we have:
[tex]\[ 6x = 30 \][/tex]

Final Step: Solve for [tex]\(x\)[/tex]

To find [tex]\(x\)[/tex], divide both sides by 6:
[tex]\[ x = \frac{30}{6} \][/tex]
[tex]\[ x = 5 \][/tex]

So, the solution to the equation [tex]\(7(x-2) = x + 16\)[/tex] is [tex]\(x = 5\)[/tex].