# Ch 7: Problems with Algebraic Expressions and Equations

### About This Chapter

## Problems with Algebraic Expressions and Equations - Chapter Summary

Let our video lessons show you how to combine like terms and simplify algebraic expressions, as well as solve equations using a variety of mathematical principles. Experienced instructors can give you sample equations to ready you for the NY Integrated Algebra Regents Exam. By the end of the chapter, you'll learn how to:

- Evaluate simple algebraic expressions
- Combine like terms in algebraic expressions
- Write equations with inequalities
- Solve one-step equations
- Solve equations using the addition and multiplication principles
- Evaluate equations with parentheses
- Translate words to algebraic expressions
- Solve equations with multiple steps

The chapter breaks up these concepts into short and engaging video lessons. Self-assessment quizzes are modeled after problems you may encounter on the NY Regents exam. You can also find lesson transcripts and key terms that allow you to better understand the chapter.

### Problems with Algebraic Expressions and Equations Objectives

The Integrated Algebra Regents Exam is one of five tests that you must pass to earn New York's Regents Diploma. This particular exam is composed of approximately 40 questions broken into four parts. You'll have three hours to complete the test and must score a 65 or better to pass. Much of the exam is multiple choice, but you'll need to fill in your answers for some of the questions. Important algebra topics covered on the test include operations, variables, expressions, equations, inequalities, number theory and probability.

### 1. Expressing Relationships as Algebraic Expressions

What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.

### 2. Evaluating Simple Algebraic Expressions

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

### 3. Combining Like Terms in Algebraic Expressions

When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions.

### 4. Practice Simplifying Algebraic Expressions

In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify.

### 5. Negative Signs and Simplifying Algebraic Expressions

Don't let negative signs get you down. In this lesson, we'll stay positive as we practice simplifying algebraic expressions that have those tricky negative signs.

### 6. Writing Equations with Inequalities: Open Sentences and True/False Statements

After watching this video lesson you will be able to write open sentences and true or false statements that use inequalities. You will also be able to solve and/or determine whether a particular inequality is true or false.

### 7. Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation.

### 8. Defining, Translating, & Solving One-Step Equations

Watch this video lesson to learn how you can write a simple math equation when you are given a word problem. Learn how to translate words into math symbols. Learn the shortcuts to remember.

### 9. Solving Equations Using the Addition Principle

In algebra, we have certain principles that we use to help us solve equations quickly and easily. The addition principle is one of them. Watch this video lesson to learn how you can apply it to solve your equations.

### 10. Solving Equations Using the Multiplication Principle

When it comes to solving equations in algebra, one of the essential skills you need is the ability to multiply. Watch this video lesson to learn how you can use the multiplication principle to isolate your variable.

### 11. Solving Equations Using Both Addition and Multiplication Principles

Most times in algebra, to solve for your variable, you will need to perform more than one operation to get your answer. Watch this video lesson to learn the proper steps to take to solve these equations.

### 12. Collecting Like Terms On One Side of an Equation

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

### 13. Solving Equations Containing Parentheses

When we have parentheses in our equations it changes the way we solve them. Now we have an added step to do to remove those parentheses. Watch this video lesson to learn how it is done.

### 14. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

### 15. How to Solve One-Step Algebra Equations in Word Problems

Word problems may be considered the most evil math invention ever, but never fear! Just watch this video lesson and you will know how to methodically translate these word problems into simple math and then to solve it.

### 16. How to Solve Equations with Multiple Steps

In algebra, when you want to solve an equation for a particular variable, you will need to perform multiple steps that include adding, subtracting, multiplying, and dividing. Watch this video lesson to learn the order you need to do these steps.

### 17. How to Solve Multi-Step Algebra Equations in Word Problems

After watching this video lesson, you will be able to solve word problems like a pro. Learn how to setup your problem, write your equations and then solve your equations to find your answer.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards