Question

lesson 3 practice problems

1. in this hanger, the weight of the triangle is x and the weight of the square is y.

image of hanger
a. write an equation using x and y to represent the hanger.
b. if x is 6, what is y?

1. andre and diego were each trying to solve 2x + 6 = 3x − 8. describe the first step they each make to the equation.

a. the result of andre’s first step was -x + 6 = -8.
b. the result of diego’s first step was 6 = x − 8.

Explanation:

Problem 1a:

Step1: Count weights per side

Left: $1x + 3y$, Right: $4x + 1y$

Step2: Set sides equal (balanced hanger)

$x + 3y = 4x + y$

Step3: Simplify the equation

Subtract $x+y$ from both sides: $2y = 3x$

Problem 1b:

Step1: Substitute $x=6$ into equation

$2y = 3(6)$

Step2: Calculate right-hand side

$2y = 18$

Step3: Solve for $y$

$y = \frac{18}{2} = 9$

Problem 2a:

Step1: Compare original and new equation

Original: $2x+6=3x-8$, New: $-x+6=-8$

Step2: Identify the operation

Subtract $3x$ from both sides.

Problem 2b:

Step1: Compare original and new equation

Original: $2x+6=3x-8$, New: $6=x-8$

Step2: Identify the operation

Subtract $2x$ from both sides.

Answer:

1a. $2y = 3x$ (or equivalent $x + 3y = 4x + y$)
1b. $9$
2a. Subtract $3x$ from both sides of the equation.
2b. Subtract $2x$ from both sides of the equation.