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Chapter 0: Problem 145

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 in which the highest power of the variable is 1, it can be written in the form \(ax + b = 0\). An example is \(2x - 3 = 0\), which has a solution \(x = 1.5\).

Step by step solution

01

Definition of a Linear Equation in One Variable

A linear equation in one variable is an equation in which the highest power of the variable is 1. It can be written in the general form \( ax + b = 0 \), where \( a \) and \( b \) are real numbers, and \( a \) is not equal to 0.
02

Example of a Linear Equation in One Variable

Now, let's provide an example. An example of a linear equation in one variable could be something like \( 2x - 3 = 0 \). Here, \( x \) is the variable, \(2\) is the coefficient of \( x \), and \(-3\) is the constant. Solving this equation for \( x \) would give us the solution \( x = 1.5 \).

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Most popular questions from this chapter

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{2 x+3}{x+1} \cdot \frac{x^{2}+4 x-5}{2 x^{2}+x-3}\right)-\frac{2}{x+2}$$

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. To earn an A in a course, you must have a final average of at least \(90 \% .\) On the first four examinations, you have grades of \(86 \%, 88 \%, 92 \%,\) and \(84 \% .\) If the final examination counts as two grades, what must you get on the final to earn an A in the course?

How is the quadratic formula derived?
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