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. a. ( x + 6 = 16 ); ( x = 10 ) b. ( x + 10 = 6 ); ( x = -4 ) c. ( x = 6 + 10 ); ( x = 16 ) d. ( x + 6 = 10 ); ( x = 4 )

Explanation:

Step1: Analyze the balance model

The left side has a square (representing \( x \)) and 6 circles. The right side has 10 circles. So the equation is \( x + 6 = 10 \)? Wait, no, wait. Wait, looking at the image again: Wait, the top part (left side of balance) has 1 square and 6 circles? Wait, no, maybe I miscounted. Wait, the bottom part (right side) has 10 circles? Wait, no, let's re-express. Wait, the balance: left side (top) is square (\( x \)) plus 6 circles? Wait, no, the top left: square (x) and 6 circles? Wait, no, the bottom right has 10 circles? Wait, no, maybe the left side is \( x + 6 \) and the right side is 10? Wait, no, the options: Let's check the options. Option D is \( x + 6 = 10 \), \( x = 4 \)? Wait, no, wait the original problem: Wait, the balance: top left: square (x) and 6 circles? Wait, no, the bottom right has 10 circles? Wait, no, maybe I made a mistake. Wait, the correct equation: Let's see the number of circles. Top left: 6 circles and 1 square (x). Bottom right: 10 circles. So the equation is \( x + 6 = 10 \). Then solving: \( x = 10 - 6 = 4 \). So the equation is \( x + 6 = 10 \), solution \( x = 4 \), which is option D? Wait, no, wait the options: Option D is \( x + 6 = 10 \); \( x = 4 \). Wait, but let's check again. Wait, maybe the left side is square (x) plus 6 circles, right side is 10 circles. So \( x + 6 = 10 \), so \( x = 10 - 6 = 4 \). So the correct option is D? Wait, no, wait the options: A is \( x + 6 = 16 \); \( x = 10 \). B is \( x + 10 = 6 \); \( x = -4 \). C is \( x = 6 + 10 \); \( x = 16 \). D is \( x + 6 = 10 \); \( x = 4 \). So let's count the circles. Top left: 6 circles and 1 square. Bottom right: 10 circles. So the balance means \( x + 6 = 10 \). Solving: subtract 6 from both sides: \( x = 10 - 6 = 4 \). So the correct option is D. Wait, but let's confirm. So the equation is \( x + 6 = 10 \), solution \( x = 4 \), which is option D.

Step2: Solve the equation

Given \( x + 6 = 10 \), subtract 6 from both sides: \( x = 10 - 6 = 4 \). So the equation is \( x + 6 = 10 \) and \( x = 4 \), which matches option D.

Answer:

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