Question

select the correct answer.
create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.
image of a balance beam with a square and 6 circles on one side, 10 circles on the other side
a. ( x + 6 = 10 ); ( x = 4 )
b. ( x + 10 = 6 ); ( x = -4 )
c. ( x = 6 + 10 ); ( x = 16 )
d. ( x + 6 = 16 ); ( x = 10 )

Explanation:

Step1: Count circles on each side

Left side (with square): 6 circles. Right side: 10? Wait, no, let's recount. Wait the left stack: top 1, middle 2, bottom 3? Wait 1+2+3=6? Wait no, the left stack (with square) has 6 circles? Wait the right stack: top 1, middle 2, bottom 3, and then another row? Wait no, the right stack: let's count. Top 1, then 2, then 3, then 4? Wait 1+2+3+4=10? No, wait the image: left side (square + circles): the circle stack is 6? Wait no, the left circle stack: 1 (top) + 2 (middle) + 3 (bottom) = 6? Wait the right circle stack: 1 + 2 + 3 + 4 = 10? No, wait the balance: left is square (x) + 6 circles, right is 10 circles? No, wait the options: A is x+6=10, x=4. Wait no, maybe I miscounted. Wait the left circle stack: 6 circles (1+2+3=6), right circle stack: 10? No, wait the right stack: let's see, the right has 1 (top), 2, 3, 4? Wait 1+2+3+4=10? No, 1+2+3=6, 1+2+3+4=10? Wait no, the left stack (with square) has 6 circles, right stack has 10? No, the options: A is x+6=10, x=4. Wait but let's check the equation. The balance means left (x + 6 circles) equals right (10 circles)? No, wait the right stack: maybe 10? Wait no, the right stack: 1 (top), 2, 3, 4? Wait 1+2+3+4=10? No, 1+2+3=6, 1+2+3+4=10? Wait the left is x + 6, right is 10? Then equation x+6=10, x=4. But wait the options: A is x+6=10, x=4. Wait but let's check again. Wait maybe the right stack is 10? Wait no, maybe I made a mistake. Wait the left circle stack: 6 (1+2+3), right circle stack: 10 (1+2+3+4)? No, 1+2+3=6, 1+2+3+4=10. So left: x + 6, right: 10. So equation x+6=10, solve x=10-6=4. So option A.
Wait no, wait the right stack: let's count the circles. The right stack: top 1, then 2, then 3, then 4? Wait the image: left stack (with square) has 6 circles (1+2+3), right stack has 10? Wait no, the right stack: 1 (top), 2, 3, 4? Wait 1+2+3+4=10? No, 1+2+3=6, 1+2+3+4=10. So left: x + 6, right: 10. So equation x+6=10, x=4. So option A.

Step2: Solve the equation

For option A: \( x + 6 = 10 \). Subtract 6 from both sides: \( x = 10 - 6 = 4 \). Which matches.

Answer:

A. \( x + 6 = 10; x = 4 \)