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

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

1:45 minutes

Problem 71

Textbook Question

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

Verified step by step guidance

Distribute the numbers outside the parentheses: Multiply 3 by each term inside the first parentheses and -2 by each term inside the second parentheses.

Simplify the equation by combining like terms.

Isolate the variable term by moving constant terms to the other side of the equation.

Divide both sides of the equation by the coefficient of the variable to solve for x.

Use a graphing calculator to verify the solution by graphing the equation and checking the x-intercept.

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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 and solve these equations is essential for finding the value of the variable, in this case, x.

Graphing Calculators

Graphing calculators are powerful tools that allow users to visualize equations and perform complex calculations. They can plot graphs of functions, solve equations, and provide numerical solutions. Familiarity with using a graphing calculator is crucial for efficiently solving linear equations and interpreting their graphical representations.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. It allows for the multiplication of a single term across terms within parentheses. In the context of the given equation, applying the distributive property is necessary to simplify the expression before solving for x.