Comprehensive Guide to Algebra 2: Solving Equations and Graphing Functions

Created from Youtube video: https://www.youtube.com/watch?v=i6sbjtJjJ-Avideo

Concepts covered:Algebra 2, linear equations, quadratic equations, graphing inequalities, factoring

This video provides a comprehensive overview of basic Algebra 2 concepts, including solving linear equations, graphing inequalities, and factoring quadratic equations. It also covers methods for solving systems of equations and graphing quadratic functions in both vertex and standard forms.

Table of Contents1.Basic Concepts in Algebra 2: Solving Linear Equations 2.Solving Fractional Equations 3.Solving and Graphing Inequalities 4.Solving and Graphing Inequalities 5.Solving Absolute Value Equations

chapter

Basic Concepts in Algebra 2: Solving Linear Equations

Concepts covered:linear equations, solving for x, variables, distribution, simplification

This chapter covers basic concepts in Algebra 2, focusing on solving linear equations. It provides step-by-step examples of solving equations with variables on both sides and distributing terms to simplify and solve for x.

Question 1

Adding the same number to both sides preserves equality.

Question 2

What is the result of distributing -2 in -2(3x+1)?

Question 3

What is the first step to solve 5x-4=11?

Question 4

CASE STUDY: An engineer is trying to balance a chemical equation and needs to solve 4x + 7 = 15x - 2.

All of the following are correct steps except...

Question 5

CASE STUDY: A financial analyst is solving the equation 3x - 5 = 2x + 8 to find the break-even point.

Select three correct steps out of the following...

chapter

Solving Fractional Equations

Concepts covered:fractions, common denominator, cross-multiplication, simplifying equations, solving for x

This chapter explains how to solve equations involving fractions by using common denominators and cross-multiplication. It provides step-by-step examples to illustrate the process of simplifying and solving for x in different types of fractional equations.

Question 6

Cross multiplication is used when both sides are fractions.

Question 7

What is 6 times 1/2 in the equation?

Question 8

What is the common denominator of 2 and 3?

Question 9

CASE STUDY: A company has 2/3 of its budget allocated to marketing and 1/4 to research. They need to determine the total budget if the marketing budget is $3000.

All of the following are correct applications of solving for the total budget except...

Question 10

CASE STUDY: A student is solving the equation 3/4x + 2 = 5. They need to isolate x.

Select three correct steps to solve for x out of the following...

chapter

Solving and Graphing Inequalities

Concepts covered:inequalities, number line, interval notation, open circle, closed circle

This chapter explains how to solve inequalities, graph the solutions on a number line, and represent them using interval notation. It covers various examples, detailing the steps to manipulate inequalities and the rules for using open and closed circles on a number line.

Question 11

Dividing by a negative number reverses inequality signs.

Question 12

How do you graph x > 3?

Question 13

What happens when dividing by a negative number?

Question 14

CASE STUDY: An engineer is solving the inequality -2x + 4 ≤ 8. They need to represent the solution on a number line.

All of the following are correct applications except...

Question 15

CASE STUDY: A researcher is working with the inequality x/2 - 1 ≥ 0. They need to graph the solution and use interval notation.

Select three correct representations of the solution.

chapter

Solving and Graphing Inequalities

Concepts covered:inequalities, number line, interval notation, compound inequality, graphing

This chapter explains how to solve and graph two inequalities on a number line, and how to represent the solutions using interval notation. It also covers solving a compound inequality simultaneously and plotting the solution on a number line.

Question 16

x > 3 is represented with a closed circle on a number line.

Question 17

How do you graph x > 3 on a number line?

Question 18

What is the solution for 2x + 5 ≤ -1?

Question 19

CASE STUDY: A company needs to determine the range of acceptable production rates. The inequality is 6x + 8 < 20 and 2x + 3 > 7. Solve for x and represent the solution in interval notation.

All of the following are correct applications except?

Question 20

CASE STUDY: A financial analyst is setting investment limits. The inequality is 3x + 5 ≤ 20 and 2x - 3 > 1. Solve for x and represent the solution in interval notation.

Select three correct solutions out of the following.

chapter

Solving Absolute Value Equations

Concepts covered:absolute value, equations, solving, non-negative, properties

This chapter explains how to solve equations involving absolute values by breaking them into two separate equations. It also emphasizes the properties of absolute value expressions, highlighting that they always yield non-negative results.

Question 21

To solve |2x - 3| = 6, set 2x - 3 to 6 and -6.

Question 22

Solve for x: |2x - 3| = 6.

Question 23

Solve for x: |x| = 4.

Question 24

CASE STUDY: A student is given the equation |3x - 2| = 7/5. They correctly isolate the absolute value expression and split it into two equations: 3x - 2 = 7/5 and 3x - 2 = -7/5.

All of the following are correct steps except:

Question 25

CASE STUDY: A student is working on the equation |x| = 4. They know they need to write two separate equations to solve for x.

Select three correct values of x:

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