Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 70

Chapter 3, Problem 70

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

Verified step by step guidance

First, simplify both sides of the equation by combining like terms. On the left side, combine the terms involving $ x $ and the constant terms separately: $ 7x - 2x + 4 - 5 $.

Rewrite the simplified equation so that it looks like $ \text{(simplified left side)} = 3x + 1 $.

Next, use the graphing calculator to graph the two expressions as separate functions: $ y = \text{(simplified left side)} $ and $ y = 3x + 1 $.

Find the point(s) where the two graphs intersect. The $ x $-coordinate(s) of the intersection point(s) represent the solution(s) to the equation.

Verify the solution by substituting the $ x $-value(s) back into the original equation to ensure both sides are equal.

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Key Concepts

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

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, in 7x - 2x, both terms contain x, so they can be combined to 5x. This step simplifies the equation and makes it easier to solve.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This typically involves isolating the variable on one side by performing inverse operations such as addition, subtraction, multiplication, or division. The goal is to simplify the equation to the form x = a number.

Using a Graphing Calculator

A graphing calculator can solve equations by graphing both sides as functions and finding their intersection point. This visual method helps identify the solution where the two expressions are equal. It is especially useful for checking work or solving more complex equations quickly.

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Related Practice

Textbook Question

Graph each function.

$ƒ (x) = - √ x - 2$

Textbook Question

Graph each function.

$ƒ (x) = ∣ x ∣ - 3$

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Textbook Question

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

Textbook Question

Graph each function.

$ƒ (x) = - ∣ x ∣$

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Textbook Question

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15

Textbook Question

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. g(x)=(x+2)²