Question

name: balance equations task each triangle = 3 each square = x 1. write an equation for each balance. a. x + 3 = 8 b. 12 = 2y c. 4z = 11 d. 2. explain how to reason with each diagram to find the value of the variable. a.

Explanation:

Step1: Analyze Diagram A

The left - hand side has a square (value $x$) and a block of value 3, and the right - hand side has a block of value 8. So the equation is $x + 3=8$. To solve for $x$, we use the subtraction property of equality. Subtract 3 from both sides: $x+3 - 3=8 - 3$, so $x = 5$.

Step2: Analyze Diagram B

The left - hand side has a block of value 12 and the right - hand side has two hexagons (each of value $y$), so the equation is $12 = 2y$. Using the division property of equality, divide both sides by 2: $\frac{12}{2}=\frac{2y}{2}$, so $y = 6$.

Step3: Analyze Diagram C

The left - hand side has a block of value 11 and the right - hand side has four triangles (each of value 3). The equation should be $4\times3=11$ which is incorrect. It seems there is a mis - label. If we assume the correct equation based on the balance concept and the value of triangles, and let the left - hand side be $z$ and right - hand side be $4\times3 = 12$, the equation is $z=12$.

Step4: Analyze Diagram D

Since each triangle is 3 and there are 4 triangles on the right - hand side, the right - hand side has a value of $4\times3=12$. Let the left - hand side value be $w$ (assuming a new variable as it is not labeled in the problem statement clearly), the equation is $w = 12$.

Answer:

a. $x = 5$
b. $y = 6$
c. If we assume the correct balance, the value related to the left - hand side (assuming variable $z$) is $z = 12$
d. Assuming a variable $w$ for the left - hand side, $w = 12$