Algebra Class Exercises 3.3

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Match the following equations with their solutions:

m + 6 = -4 = m = -10 a - 6 = 13 = a = 19 x + 4 = -14 = x = -18 g - 9 = -19 = g = -10

Match the following operations with their inverses:

Addition = Subtraction Multiplication = Division Exponentiation = Logarithm Squaring = Square root

Match the following expressions with their errors:

x + 8 = 10 = x = 18 9 + (-3) = = 6 9 + (-9) = = 0 4 + (-1) = = 3

Match the word sentences with their corresponding equations:

4 less than a number n is -15 = n - 4 = -15 10 more than a number c is 3 = c + 10 = 3 The sum of a number y and -3 is -8 = y - 3 = -8 The difference between a number p and 6 is -14 = p - 6 = -14 Signup and view all the answers

Match the following equations that do not belong with the others:

x + 3 = -1 = Linear equation x + 1 = -5 = Linear equation x - 2 = -6 = Linear equation x - 9 = -13 = Quadratic equation Signup and view all the answers

Match the following equations with their types:

x + 3 = -5 = Linear c - 10 = 0 = Linear y^2 + 4y = 0 = Quadratic z + 2z - 6 = 0 = Linear Signup and view all the answers

Match the following scenarios with the mathematical operations needed to solve them:

Dry Ice Temperature = Addition Company Profit Last Year = Subtraction Helicopter Elevation = Addition Statue of Liberty Height = Subtraction Signup and view all the answers

Match the following algebraic solutions with their corresponding problems:

−3 = z - 8 = Find z −14 = k + 6 = Find k 9 - 3 = x = Find x −10.1 = w + 5.3 = Find w Signup and view all the answers

Match the following operations with their results:

9 + (-3) = 6 3 + (-9) = -6 4 + (-1) = 3 5 + (-5) = 0 Signup and view all the answers

Match the following perimeter problems with their corresponding values:

Perimeter = 12 cm = 3 cm Perimeter = 24.2 in. = 8.3 in. Perimeter = 34.6 ft = 5.2 ft Signup and view all the answers

Match the following measurements with their corresponding value adjustments:

Dry Ice Temperature = $-109.3°F Profit Increase = $2.54 million Helicopter to Submarine Elevation Difference = 18 meters First Jump Height = $305 ft Signup and view all the answers

Match the following temperature and height problems with their unknowns:

Outside Temperature Calculation = Outside Temperature Profit Last Year Calculation = Last Year's Profit Helicopter Elevation Calculation = Helicopter Elevation Height of Statue Calculation = Statue Height Signup and view all the answers

Match the following height and temperature expressions with their correct formulations:

Outside Temperature = Dry Ice + 184.9 = $-109.3 + 184.9$ Last Year's Profit = Current Profit - Increase = $1.38 million - $2.54 million Helicopter Elevation = Submarine Elevation + 18 = $-7 + 18$ Statue Height = Total Height - Pedestal Height = $153 - Pedestal Height Signup and view all the answers

Match the following equations with their scenario descriptions:

x - $2.54 million = 1.38 = Profit Calculation -7 + 18 = x = Helicopter Elevation x + y = 153 = Statue of Liberty Height 184.9 + x = -109.3 = Outside Temperature Signup and view all the answers

Match each scenario with its respective number:

Dry Ice Temperature = $-109.3°F Profit = $1.38 million Helicopter Elevation = $-7$ meters Height of Statue = Unknown Signup and view all the answers

Match the following increment and decrement operations with their context:

First Jump to Second Jump Difference = Addition Company Profit Change = Increase Dry Ice Temperature Reference Adjustment = Decrease Helicopter to Submarine Elevation = Subtraction Signup and view all the answers

Match the distance with the correct bus travel scenario:

Bus travels from Stanton to Boatesville = 24 kilometers Bus travels from Boatesville to Stanton = 65 kilometers Total distance between Stanton and Boatesville = 89 kilometers Distance remaining after first leg of the journey = 41 kilometers Signup and view all the answers

Match the geometric property with its value:

Sum of angles in a triangle = 180 degrees Measure of the first angle = 30.3 degrees Measure of the second angle = 40.8 degrees Missing angle = 109.9 degrees Signup and view all the answers

Match the skateboard score with the corresponding round:

Round 1 = 63.43 points Round 2 = 87.15 points Round 3 = 81.96 points Round 4 = Score needed to win Signup and view all the answers

Match the mathematical expression with its operation:

−7 × 8 = −56 6 × (−12) = −72 18 ÷ (−2) = −9 −26 ÷ 4 = −6.5 Signup and view all the answers

Match the absolute value equation with its solution:

|x|=2 = x=2 or x=−2 |x|−2=4 = x=6 or x=−6 |x| + 5=18 = x=13 or x=−13 x + 6 = 2 = x=−4 Signup and view all the answers

Match the fraction with its total count of students:

Three-fourths of 144 students = 108 students Female students who voted for you = 49 students Total students in the class = 144 students Students who did not vote = 36 students Signup and view all the answers

Match the second jump height to its value:

First jump height = $5$ m Second jump height = $3$ m Third jump height = $7$ m Fourth jump height = $4$ m Signup and view all the answers

Match the critical thinking problem with its equation:

Find the value of 2x−1 when x + 6 = 2 = x=−4 ∣x∣=2 = x=2 or x=−2 ∣x∣−2=4 = x=6 or x=−6 ∣x∣ + 5 = 18 = x=13 or x=−13 Signup and view all the answers

Study Notes

Exercises 3.3

Vocabulary:
- Property used to solve m + 6 = -4: Addition property of equality
- Two inverse operations: addition and subtraction, multiplication and division
- Are m + 3 = -5 and m = -2 equivalent?: No, they are not equivalent equations.
- Which equation does not belong?: This question lacks context.
Practice and Problem Solving:
- Solve equations, including those with integer, decimal, and fraction coefficients. Check solutions.
Error Analysis:
- Identify and correct errors in solving equations.
Word Sentence to Equation:
- Translate word problems into equations representing relationships between variables.
Solve equations: Examples provided include single-variable equations.
Dry Ice Example:
- Equation: Outside temperature = -109.3°F + 184.9°F
Profit Example
- Equation: profit last year = $1.38 million - 2.54 million
Helicopter Example:
- Equation: Helicopter's elevation - (-7 meters)= 18 meters

Geometry

Perimeter: Find unknown side lengths given other side lengths and perimeter.
Statue of Liberty
- Equation: Height of Statue + Height of Platform = 153 feet
Bungee Jumping: Solve for the missing jump height given the other jump height relation.
Travel:
- Equation: Distance traveled + remaining distance= Total distance
Geometry
- The sum of angles in a triangle is 180 degrees.
- Solve missing angle scenarios.
Skateboarding
- Find the score needed in the fourth round.
Critical Thinking:
- Find the value of 2x - 1, given x + 6 = 2

Fair Game Review (Previous Concepts)

Multiply/Divide exercises for integers.
Multiple Choice: Calculate how many female students voted for the class president. (Three quarters of the class voted and five ninths of those are female.)

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz focuses on key concepts in algebra, particularly on solving equations, properties of equality, and error analysis. It includes practice problems related to various coefficients and the translation of word problems into equations. Test your understanding of these foundational algebraic concepts.