Lesson 12: Practice Problems

Problem 1

In this hanger, the weight of the triangle is $x$ and the weight of the square is $y$ .

A balanced hanger diagram with 1 triangle and 3 squares on the left and 4 triangles and 1 square on the right

Write an equation using $x$ and $y$ to represent the hanger.
If $x$ is 6, what is $y$ ?

Problem 2

Andre and Diego were each trying to solve $2 x + 6 = 3 x - 8$ . Describe the first step they each make to the equation.

The result of Andre’s first step was $- x + 6 = - 8$ .
The result of Diego’s first step was $6 = x - 8$ .

Problem 3

Match each set of equations with the move that turned the first equation into the second.

$6 x + 9 = 4 x - 3$

$2 x + 9 = - 3$
$- 4 (5 x - 7) = - 18$

$5 x - 7 = 4.5$
$8 - 10 x = 7 + 5 x$

$4 - 10 x = 3 + 5 x$
$\frac{- 5 x}{4} = 4$

$5 x = - 16$
$12 x + 4 = 20 x + 24$

$3 x + 1 = 5 x + 6$

Multiply both sides by $\frac{- 1}{4}$
Multiply both sides by $- 4$
Multiply both sides by $\frac{1}{4}$
Add $- 4 x$ to both sides
Add $- 4$ to both sides

Problem 4

What is the weight of a square if a triangle weighs 4 grams?

Explain your reasoning.

A balanced hanger diagram with a triangle and 2 squares on the left and 3 triangles and square on the right

Problem 5

Here is a balanced hanger diagram.

A balanced hanger diagram with 4 squares, 2 triangles, 2 circles on the left and 2 squares, 1 triangle, 3 circles on the right

Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and $x$ represents the weight of each square. Select all equations that represent the hanger.

$x + x + x + x + 11 = x + 11.5$
$2 x = 0.5$
$4 x + 5 + 6 = 2 x + 2.5 + 6$
$2 x + 2.5 = 3$
$4 x + 2.5 + 2.5 + 3 + 3 = 2 x + 2.5 + 3 + 3 + 3$