On the left side of a line, there are 2 rectangles, each labeled x, and 7 squares, each labeled negative 1. On the right side of the line, there are 3 squares, each labeled 1.

Question

The algebra tiles represent an equation.

What is the solution to the equation?

(1 point)
Responses

x=−2
x equals negative 2

x=10
x equals 10

x=2
x equals 2

x=5

Answer 1

To solve the equation represented by the algebra tiles, we first interpret the tiles on both sides of the line.

On the left side:

• There are 2 rectangles labeled \( x \), which represents \( 2x \).
• There are 7 squares labeled \( -1 \), which represents \( -7 \).

Combining these, the left side translates to: \[ 2x - 7 \]

On the right side:

• There are 3 squares labeled \( 1 \), which represents \( 3 \).

Setting the left side equal to the right side gives us the equation: \[ 2x - 7 = 3 \]

Now, we can solve for \( x \):

1. Add 7 to both sides: \[ 2x - 7 + 7 = 3 + 7 \] \[ 2x = 10 \]

2. Divide both sides by 2: \[ x = \frac{10}{2} \] \[ x = 5 \]

Therefore, the solution to the equation is: \[ x = 5 \]

So the correct response is: x=5