Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
16w+9=13w+18
3w+9=18
Add 13w to both sides
Subtract 13w from both sides
Multiply both sides by 13w
Divide both sides by 13w
Apply the distributive property
3w=
Subtract 9 from both sides
w=
Divide both sides by 3

Answer 1

Let's solve the equation step by step, filling in the missing terms and descriptions as requested.

Given Equation: \( 16w + 9 = 13w + 18 \)

Step 1:
Subtract \( 13w \) from both sides.

• Description: Subtract 13w from both sides
  \[ 16w - 13w + 9 = 18 \]
  \[ 3w + 9 = 18 \]

Step 2:
Subtract 9 from both sides.

• Description: Subtract 9 from both sides
  \[ 3w + 9 - 9 = 18 - 9 \]
  \[ 3w = 9 \]

Step 3:
Divide both sides by 3.

• Description: Divide both sides by 3
  \[ \frac{3w}{3} = \frac{9}{3} \]
  \[ w = 3 \]

Now let's summarize:

1. Start with the equation \( 16w + 9 = 13w + 18 \)
2. Subtract \( 13w \) from both sides → \( 3w + 9 = 18 \)
3. Subtract 9 from both sides → \( 3w = 9 \)
4. Divide both sides by 3 → \( w = 3 \)

So the complete solution is:

• \( 3w = 9 \)
• \( w = 3 \)

Descriptions filled in:

• Subtract 13w from both sides
• Subtract 9 from both sides
• Divide both sides by 3