Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:10 minutes

Problem 70

Textbook Question

Use a graphing calculator to solve each linear equation. 7x-2x+ 4-5=3x+1

Verified step by step guidance

Combine like terms on the left side of the equation: \(7x - 2x + 4 - 5 = 3x + 1\).

Simplify the left side: \(5x - 1 = 3x + 1\).

Subtract \(3x\) from both sides to get the variable terms on one side: \(5x - 3x - 1 = 1\).

Simplify the equation: \(2x - 1 = 1\).

Add 1 to both sides to isolate the term with \(x\): \(2x = 2\).

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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. Understanding how to manipulate these equations is essential for finding the value of the variable, which is often the goal in algebraic problems.

Graphing Calculators

Graphing calculators are powerful tools that can plot equations, find intersections, and solve equations numerically. They allow students to visualize the relationship between variables and can simplify the process of solving complex equations. Familiarity with the functions of a graphing calculator is crucial for efficiently solving linear equations.

Combining Like Terms

Combining like terms is a fundamental algebraic skill that involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This process is essential for solving equations, as it helps to reduce the complexity of the equation, making it easier to isolate the variable and find its value.