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Chapter 1: Problem 107

What is a linear equation in one variable? Give an example of this type of equation.

Short Answer

Expert verified
A linear equation in one variable is an equation that can be written in the form \(ax + b = 0\), where \(a\) and \(b\) are numbers and \(x\) is the variable. The highest power of the variable is 1. An example is \(2x + 3 = 0\).

Step by step solution

01

Defining Linear Equation

A linear equation in one variable is an equation that can be written in the form \(ax + b = 0\), where \(a\) and \(b\) are numbers and \(x\) is the variable. The highest power of the variable \(x\) is 1, which makes the graph of any such equation a straight line.
02

Creating an Example

An example of a linear equation in one variable can be \(2x + 3 = 0\). In this equation, \(x\) is the variable, while \(2\) and \(3\) are the coefficients. It is a linear equation because the power of \(x\) is 1.

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Solve absolute value inequality. \(\left|\frac{2 x+2}{4}\right| \geq 2\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(7-\frac{4}{5} x<\frac{3}{5}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Solve without squaring both sides: $$\text { Solve for } x: x^{6}+x^{3}-2 x^{2}-0$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(-4(x+2)>3 x+20\)
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