Question

label the arrows to describe each move.
$x = 4$
$3x = 12$
$3x + 4 = 16$
$\frac{3}{2}x + 2 = 8$

Explanation:

Step1: Analyze \( x = 4 \) to \( 3x = 12 \)

To get from \( x = 4 \) to \( 3x = 12 \), we multiply both sides of the equation \( x = 4 \) by 3. So the operation is "Multiply both sides by 3".

Step2: Analyze \( 3x = 12 \) to \( 3x + 4 = 16 \)

To get from \( 3x = 12 \) to \( 3x + 4 = 16 \), we add 4 to both sides of the equation \( 3x = 12 \). So the operation is "Add 4 to both sides".

Step3: Analyze \( 3x + 4 = 16 \) to \( \frac{3}{2}x + 2 = 8 \)

To get from \( 3x + 4 = 16 \) to \( \frac{3}{2}x + 2 = 8 \), we divide both sides of the equation \( 3x + 4 = 16 \) by 2. So the operation is "Divide both sides by 2".

Step4: Analyze \( \frac{3}{2}x + 2 = 8 \) to \( 3x + 4 = 16 \)

To get from \( \frac{3}{2}x + 2 = 8 \) to \( 3x + 4 = 16 \), we multiply both sides of the equation \( \frac{3}{2}x + 2 = 8 \) by 2. So the operation is "Multiply both sides by 2".

Step5: Analyze \( 3x + 4 = 16 \) to \( 3x = 12 \)

To get from \( 3x + 4 = 16 \) to \( 3x = 12 \), we subtract 4 from both sides of the equation \( 3x + 4 = 16 \). So the operation is "Subtract 4 from both sides".

Step6: Analyze \( 3x = 12 \) to \( x = 4 \)

To get from \( 3x = 12 \) to \( x = 4 \), we divide both sides of the equation \( 3x = 12 \) by 3. So the operation is "Divide both sides by 3".

Answer:

• \( x = 4 \) to \( 3x = 12 \): Multiply both sides by 3
• \( 3x = 12 \) to \( 3x + 4 = 16 \): Add 4 to both sides
• \( 3x + 4 = 16 \) to \( \frac{3}{2}x + 2 = 8 \): Divide both sides by 2
• \( \frac{3}{2}x + 2 = 8 \) to \( 3x + 4 = 16 \): Multiply both sides by 2
• \( 3x + 4 = 16 \) to \( 3x = 12 \): Subtract 4 from both sides
• \( 3x = 12 \) to \( x = 4 \): Divide both sides by 3