Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

1:33 minutes

Problem 1b

Textbook Question

In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving a linear equation involves isolating the variable to find its value, which satisfies the equation.

Isolating the Variable

Isolating the variable is a fundamental technique in solving linear equations. This process involves performing operations such as addition, subtraction, multiplication, or division to get the variable alone on one side of the equation. For example, in the equation 4x + 9 = 33, you would first subtract 9 from both sides to simplify the equation.

Checking Solutions

Checking solutions is the process of substituting the found value of the variable back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation, confirming that no errors were made during the solving process. For instance, if x = 6 is found, substituting it back into 4x + 9 should yield 33.