Honor's Pre-Algebra Chapter 8 Test Review
Short Answer
Solve the equation. Show your work.
1.
2.
3.
4.
5.
6.
Solve the inequality. Show your work.
7.
8.
9.
10.
Solve the inequality. Show your work. Graph the solution on a number line.
11.
12.
13.
14.
15.
16.
17. Define a variable and write an equation to find each number. Then solve. (#17 & #18) Show your work.
A triangle has two equal sides, and the third side of the triangle is 5 feet shorter than the first side. If the
perimeter of the triangle is 40 feet, find the dimensions of each side.
18. The perimeter of a rectangle is 60 feet. Find the dimensions of the rectangle if the length is 6 feet shorter than
twice the width.
Honor's Pre-Algebra Chapter 8 Test Review
Answer Section
SHORT ANSWER
1. ANS:
4
Write an equivalent equation with the variables on one side. Then solve the equation.
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.1 Solve equations with variables on each side.
NAT: NA 2 | NA 6
STA: PFA 9
TOP: Solve equations with variables on each side.
KEY: Solve Equations | Variables
2. ANS:
–22
Use the Distributive Property to evaluate the expressions involving parentheses. Group the variables on one
side of the equation and solve.
PTS:
OBJ:
STA:
KEY:
3. ANS:
1
DIF: Average
REF: Lesson 8-2
8-2.1 Solve equations that involve grouping symbols.
NAT: NA 2 | NA 6 | NA 3
PFA 8 | PFA 9
TOP: Solve equations that involve grouping symbols.
Solve Equations | Grouping Symbols
Use the Distributive Property to evaluate the expressions involving parentheses. Group the variables on one
side of the equation and solve.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Identify equations that have no solution or an infinite number of solutions.
NAT: NA 2 | NA 6 | NA 3
STA: PFA 11
TOP: Identify equations that have no solution or an infinite number of solutions.
KEY: Equations | Solutions | Infinite Solutions
4. ANS:
all numbers
Use the Distributive Property to evaluate the expressions involving parentheses. Group the variables on one
side of the equation and solve.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Identify equations that have no solution or an infinite number of solutions.
NAT: NA 2 | NA 6 | NA 3
STA: PFA 11
TOP: Identify equations that have no solution or an infinite number of solutions.
KEY: Equations | Solutions | Infinite Solutions
5. ANS:
all numbers
Use the Distributive Property to evaluate the expressions involving parentheses. Group the variables on one
side of the equation and solve.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Identify equations that have no solution or an infinite number of solutions.
NAT: NA 2 | NA 6 | NA 3
STA: PFA 11
TOP: Identify equations that have no solution or an infinite number of solutions.
KEY: Equations | Solutions | Infinite Solutions
6. ANS:
32
Write an equivalent equation with the variables on one side. Then solve the equation.
PTS:
OBJ:
STA:
KEY:
7. ANS:
1
DIF: Average
REF: Lesson 8-1
8-1.1 Solve equations with variables on each side.
NAT: NA 2 | NA 6
PFA 9
TOP: Solve equations with variables on each side.
Solve Equations | Variables
Add the constant on the left to both sides of the inequality to solve.
PTS:
OBJ:
NAT:
TOP:
KEY:
8. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.1 Solve equations by using the Addition Properties of Inequality.
NA 1 | NA 6 | NA 8 | NA 2
Solve inequalities by using the Addition Property of Inequality.
Solve Inequalities | Addition Property
Add the constant on the right to both sides of the inequality to solve.
PTS:
OBJ:
NAT:
TOP:
KEY:
9. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.1 Solve equations by using the Addition Properties of Inequality.
NA 1 | NA 6 | NA 8 | NA 2
Solve inequalities by using the Addition Property of Inequality.
Solve Inequalities | Addition Property
Subtract the constant on the left from both sides of the inequality to solve.
PTS:
OBJ:
NAT:
TOP:
KEY:
10. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.2 Solve equations by using the Subtraction Properties of Inequality.
NA 1 | NA 6 | NA 8 | NA 2
Solve inequalities by using the Subtraction Property of Inequality.
Solve Inequalities | Subtraction Property
Subtract the constant on the right from both sides of the inequality to solve.
PTS:
OBJ:
NAT:
TOP:
KEY:
11. ANS:
1
DIF: Average
REF: Lesson 8-4
8-4.2 Solve equations by using the Subtraction Properties of Inequality.
NA 1 | NA 6 | NA 8 | NA 2
Solve inequalities by using the Subtraction Property of Inequality.
Solve Inequalities | Subtraction Property
0
10
20
30
40
50
Multiply both sides of the inequality by the number in the denominator to solve.
PTS:
OBJ:
NAT:
TOP:
12. ANS:
–12
1
DIF: Average
REF: Lesson 8-5
8-5.1 Solve inequalities by multiplying by a positive number.
NA 1 | NA 6 | NA 2
STA: PFA 9
Solve inequalities by multiplying by a positive number.
KEY: Solve Inequalities | Multiplication
–8
–4
0
4
8
12
Divide both sides of the equation by the coefficient of a to solve.
PTS:
OBJ:
NAT:
TOP:
13. ANS:
1
DIF: Average
REF: Lesson 8-5
8-5.2 Solve inequalities by dividing by a positive number.
NA 1 | NA 6 | NA 2
STA: PFA 9
Solve inequalities by dividing by a positive number.
KEY: Solve Inequalities | Division
–50
–40
–30
–20
–10
0
Multiply both sides of the inequality by the number in the denominator to solve. Remember to reverse the
inequality sign when multiplying by a negative number.
PTS:
OBJ:
NAT:
TOP:
14. ANS:
–12
1
DIF: Average
REF: Lesson 8-5
8-5.3 Solve inequalities by multiplying by a negative number.
NA 1 | NA 6 | NA 2
STA: PFA 9
Solve inequalities by multiplying by a negative number. KEY: Solve Inequalities | Multiplication
–8
–4
0
4
8
12
Divide both sides of the equation by the coefficient of c to solve. Remember to reverse the inequality sign
when dividing by a negative number.
PTS:
OBJ:
NAT:
TOP:
15. ANS:
–70
1
DIF: Average
REF: Lesson 8-5
8-5.4 Solve inequalities by dividing by a negative number.
NA 1 | NA 6 | NA 2
STA: PFA 9
Solve inequalities by dividing by a negative number.
KEY: Solve Inequalities | Division
–56
–42
–28
–14
0
First add the constant on the right to both sides. Then, multiply both sides of the inequality by the number in
the denominator to solve. Remember to reverse the inequality sign when multiplying by a negative number.
PTS:
OBJ:
NAT:
TOP:
16. ANS:
–12
1
DIF: Average
REF: Lesson 8-6
8-6.1 Solve inequalities that involve more than one operation.
NA 1 | NA 6 | NA 9 | NA 2
STA: PFA 9
Solve inequalities that involve more than one operation. KEY: Solve Inequalities
–8
–4
0
4
8
12
First subtract the coefficient on the left from both sides. Then divide both sides of the equation by the
coefficient of b to solve.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.1 Solve inequalities that involve more than one operation.
NAT: NA 1 | NA 6 | NA 9 | NA 2
STA: PFA 9
TOP: Solve inequalities that involve more than one operation. KEY: Solve Inequalities
17. ANS:
x = 1st and 2nd side
x – 5 = 3rd side
x + x + x – 5 = 40
15 ft, 15 ft, 10 ft
The perimeter of a triangle is the sum of its three sides.
Write an equation according to the given information. Solve the equation to get the answer.
PTS: 1
DIF: Average
TOP: Solve multi-step problems.
18. ANS:
w = width
2w – 6 = length
2w + 2(2w – 6) = 60
length
ft
width
ft
REF: Lesson 8-2
OBJ: 8-2.3 Solve multi-step problems.
KEY: Multi-step | Problem Solving
Perimeter of the rectangle =
Write an equation according to the given information. Solve the equation to get the answer.
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
REF: Lesson 8-2
OBJ: 8-2.3 Solve multi-step problems.
KEY: Multi-step | Problem Solving