We can distribute the

4
1

to rewrite the left side of the equation without parentheses. What is (
4
1

·24x)+(
4
1

·36)?
4
1

(24x+36)
=
3(2x+3)

+
=
3(2x+3)

1 answer

To rewrite the expression \( 41 \cdot (24x + 36) \) without parentheses and distribute \( 41 \) across the terms inside the parentheses, you perform the following steps:

  1. Distribute \( 41 \) to \( 24x \): \[ 41 \cdot 24x = 984x \]

  2. Distribute \( 41 \) to \( 36 \): \[ 41 \cdot 36 = 1476 \]

  3. Combine both results: \[ 41 \cdot (24x + 36) = 984x + 1476 \]

Now, you also have the expression on the right side of the equation, which is given as \( 3(2x + 3) \). If you want to rewrite this expression:

  1. Distribute \( 3 \) across \( 2x \): \[ 3 \cdot 2x = 6x \]

  2. Distribute \( 3 \) across \( 3 \): \[ 3 \cdot 3 = 9 \]

  3. Combine both results: \[ 3(2x + 3) = 6x + 9 \]

Now you have two expressions:

  • Left side: \( 984x + 1476 \)
  • Right side: \( 6x + 9 \)

If you want to set these two expressions equal to each other: \[ 984x + 1476 = 6x + 9 \]

If you were solving for \( x \), you can rearrange and solve this equation accordingly.