Chapter 1: Q3. (page 30)

Determine whether the following statement is sometimes, always, or never true. Explain.
For all real numbers $a$ and $b, a \neq 0$ , the equation $|a x + b| = 0$ will have one solution.

Short Answer

Expert verified

Given statement is always true.

Since, $|a x + b| = 0$ is true when ax+b=0 which is true only for $x = - \frac{b}{a}$

So given equation is always true.

Step by step solution

- Define absolute value

Absolute value of a number is its distance from 0 on the number line.

- Meaning of ax+b=0

Distance of expression ax+b is 0 from origin.

So ax+b=0

- Find ax+b=0 has one or more solution

As ax+b=0 is a linear equation which has only one solution namely $x = - \frac{b}{a}$

So given statement is always true.

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Determine whether the following statement is sometimes, always, or never true. Explain.
For all real numbers $a$ and $b, a \neq 0$ , the equation $|a x + b| = 0$ will have one solution.

Short Answer

Step by step solution

- Define absolute value

- Meaning of ax+b=0

- Find ax+b=0 has one or more solution

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Determine whether the following statement is sometimes, always, or never true. Explain.For all real numbers aandb,a≠0, the equationax+b=0 will have one solution.

Short Answer

Step by step solution

- Define absolute value

- Meaning of ax+b=0

- Find ax+b=0 has one or more solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Applied Mathematics

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Determine whether the following statement is sometimes, always, or never true. Explain.
For all real numbers $a$ and $b, a \neq 0$ , the equation $|a x + b| = 0$ will have one solution.