Question

next, distribute the 2 to the 3. what is 2 groups of 3? write this as a single whole number. you can use the hanger diagram to help you represent this in the equation.
(diagrams: top diagram has two purple squares labeled 3, two orange hexagons labeled x, and a purple rectangle labeled 18. bottom diagram has a balance with 2(x + 3) on one side and 2x + on the other, equal to 18 and a question mark.)

Explanation:

Step1: Analyze the hanger diagram

The hanger has two \( x \)s, two 3s, and balances with 18. So the equation is \( 2x + 3 + 3 = 18 \), which simplifies to \( 2x + 6 = 18 \) or using the distributive property, \( 2(x + 3)=18 \).

Step2: Solve the equation \( 2(x + 3)=18 \)

First, divide both sides by 2: \( \frac{2(x + 3)}{2}=\frac{18}{2} \), so \( x + 3 = 9 \).
Then, subtract 3 from both sides: \( x + 3 - 3 = 9 - 3 \), so \( x = 6 \).

Answer:

\( x = 6 \)