Lesson 3: 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 From Unit 3 Lesson 11

Complete the table with values for $x$ or $y$ that make this equation true: $3 x + y = 15$ .
$x$
$2$
$6$
$0$
$3$
$y$
$3$
$0$
$8$
Create a graph, plot these points, and find the slope of the line that goes through them.

Problem 4

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 5

Select all the situations for which only zero or positive solutions make sense.

Measuring temperature in degrees Celsius at an Arctic outpost each day in January.
The height of a candle as it burns over an hour.
The elevation above sea level of a hiker descending into a canyon.
The number of students remaining in school after 6:00 p.m.
A bank account balance over a year.
The temperature in degrees Fahrenheit of an oven used on a hot summer day.