Question

level 3
instructions: model and solve each equation. type your answer as a decimal or an integer (no fractions!)
1 the model represents an equation.
what value of x makes the equation true?
type your solution into the first box!
1 x =
2 x =
3 x =
4 x =
5 x =
6 x =

Explanation:

Step1: Analyze the left side

The left side of the balance has 3 \( x \)s and 2 \( 1 \)s, so it can be represented as \( 3x + 2 \).

Step2: Analyze the right side

The right side of the balance has 1 \( x \) and 4 \( -1 \)s, so it can be represented as \( x - 4 \).

Step3: Set up the equation

Since the balance is equal, we set \( 3x + 2 = x - 4 \).

Step4: Solve for \( x \)

Subtract \( x \) from both sides: \( 3x - x + 2 = x - x - 4 \), which simplifies to \( 2x + 2 = -4 \).
Subtract 2 from both sides: \( 2x + 2 - 2 = -4 - 2 \), so \( 2x = -6 \).
Divide both sides by 2: \( \frac{2x}{2} = \frac{-6}{2} \), giving \( x = -3 \).

Answer:

\( -3 \)