Linear Expressions, Equations and Inequalities Portfolio
Use the worksheet to record your answers to the Linear Expressions, Equations and Inequalities portfolio activity. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.
Roger is a wildlife researcher who has been hired to study and track the population of bears in a national park. In Year 1 of the study, Roger determines that the park is home to x
bears. In Year 2, the population has increased to x+10
bears, and in Year 3, the population has increased to 2(x+10)
bears.
Use the Distributive Property to rewrite the bear population in Year 3 without needing to use parentheses.
The total number of bears in the park during Year 2 is 42. Write and solve a linear equation to determine how many bears were in the park during Year 1.
The total number of bears in the park during Year 3 is 50. Write and solve a linear equation to determine how many bears were in the park during Year 1. Note that this answer will not be the same as the answer you got in part b
.
During Year 4, bad weather keeps Roger from finding the exact number of bears in the park. However, he knows that y+5>38
, where y
is the number of bears in the park during Year 4. Solve the inequality, and give three possible values for y
.
Jin is a wildlife researcher hired to track the population of wolves in the same national park. In Year 1 of the study, there are z
wolves; in Year 2 of the study, there are 7+z
wolves; and in Year 3 of the study, there are 3z−3
wolves. The number of wolves in Year 2 is equal to the number of wolves in Year 3.
Write and solve a linear equation to determine the value of z
.
Jin writes an expression to describe the number of wolves in Year 4 of the study. The expression is (x+a)(x−b)
, where a
and b
are whole numbers greater than 1 and less than 10. Write an expression that could be the expression Jin uses to describe the number of wolves in the park during Year 4 of the study. Then multiply the two terms of the expression.
1. Use the Distributive Property to rewrite the bear population in Year 3 without needing to use parentheses.
2(x + 10)
= 2x + 2(10)
= 2x + 20
Therefore, the bear population in Year 3 is 2x + 20.
2. The total number of bears in the park during Year 2 is 42. Write and solve a linear equation to determine how many bears were in the park during Year 1.
x + 10 = 42
x = 42 - 10
x = 32
Therefore, the number of bears in the park during Year 1 is 32.
3. The total number of bears in the park during Year 3 is 50. Write and solve a linear equation to determine how many bears were in the park during Year 1.
2x + 20 = 50
2x = 50 - 20
2x = 30
x = 30/2
x = 15
Therefore, the number of bears in the park during Year 1 is 15.
4. Solve the inequality y + 5 > 38, and give three possible values for y.
y + 5 > 38
y > 38 - 5
y > 33
Three possible values for y could be: 34, 35, 36.
5. Write and solve a linear equation to determine the value of z.
7 + z = 3z - 3
7 + 3 = 3z - z
10 = 2z
z = 5
Therefore, the number of wolves in Year 1 is 5.
6. Write an expression that could be the expression Jin uses to describe the number of wolves in the park during Year 4 of the study.
An expression that could be used is: (z + a)(z - b), where a and b are whole numbers greater than 1 and less than 10.
If we choose a = 3 and b = 2, then the expression becomes: (z + 3)(z - 2)
Expanding the expression:
= z^2 - 2z + 3z - 6
= z^2 + z - 6