Q3. Determine whether the following ... [FREE SOLUTION]

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Chapter 1: Q3. (page 30)

Determine whether the following statement is sometimes, always, or never true. Explain.
For all real numbers $a$ and $b, a 鈮� 0$ , 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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Year	Average CPI
1950	42.1
1960	29.6
1970	38.8
1980	82.4
1990	130.7
2000	174.0

91影视

Determine whether the following statement is sometimes, always, or never true. Explain.
For all real numbers $a$ and $b, a 鈮� 0$ , 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

One App. One Place for Learning.

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91影视

Determine whether the following statement is sometimes, always, or never true. Explain.For all real numbers aandb,a鈮�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

Pure Maths

Applied Mathematics

Probability and Statistics

Geometry

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

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