Algebra Chapter Inequalities and Absolute Values
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Questions and Answers

What are the solutions for the equation $|a - 5| = 240$?

  • $a = 5 + 240$ and $a = 5 - 240$
  • $a = 245$ and $a = 5 - 240$
  • $a = 245$ and $a = -235$ (correct)
  • $a = 240$ and $a = -240$

What transformation is applied to $g(x) = |x|$ to get $h(x) = 4|x + 3|$?

  • Vertical stretch by a factor of 4 and vertical compression by a factor of 1/5
  • Horizontal shift 3 units to the right and vertical stretch by a factor of 4
  • Vertical compression by a factor of 1/5 and horizontal shift 3 units to the right
  • Horizontal shift 3 units to the left and vertical stretch by a factor of 4 (correct)

For the equation $7m + 8 = 73$, what is the calculated value of $m$?

  • $m = 65$
  • $m = 65/7$ (correct)
  • $m = 9$
  • $m = 7/65$

Which statement correctly describes the relationship between functions $f(x)$ and $g(x)$ based on their graph?

<p>$g(x)$ is a translation of $f(x)$ by 6 units to the right (D)</p> Signup and view all the answers

For the equation $4/n + 8 = 56$, what can be concluded about the value of $n$?

<p>$n$ does not produce a valid solution (B)</p> Signup and view all the answers

What is the solution for the inequality |-8a - 3| > 11?

<p>a &lt; -1.75 or a &gt; 1 (A)</p> Signup and view all the answers

Which of the following best describes the interval notation for the solution to |-4k| ≥ 11?

<p>(-∞, -11/4] U [11/4, ∞) (B)</p> Signup and view all the answers

Why does the equation |9r - 2| - 10 ≤ -73 have no solution?

<p>Absolute value cannot be less than or equal to a negative number. (B)</p> Signup and view all the answers

What is the interval notation for the solution to |3/4n + 9| < 12?

<p>(-28, 4) (A)</p> Signup and view all the answers

In solving and expressing the solution for |-8a - 3| > 11, what does the notation {a | a < -7/4 or a > 1} signify?

<p>The values of a where the inequality holds true. (A)</p> Signup and view all the answers

Flashcards

Absolute Value Inequality

An absolute value inequality involving the distance from zero, either greater than or less than a given value, usually solved by splitting the problem into two inequalities.

Interval Notation

Represents a set of numbers within a range, including the endpoints.

Set Notation

Represents all solutions that satisfy a certain condition, often using set symbols.

No Solution

When solving absolute value inequalities with the absolute value less than a negative number.

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Compound Inequality

A compound inequality with a variable between two values, creating an inclusive interval.

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Solving Absolute Value Equations

To solve an absolute value equation, we consider both positive and negative values of the expression inside the absolute value bars. For Example, if |x| = 5, then x = 5 or x = -5.

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Vertical Stretch

A vertical stretch of a graph means the graph is stretched vertically by a factor greater than 1. For example, if a graph is stretched by a factor of 2, all its y-coordinates are doubled.

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Horizontal Shift

A horizontal shift of a graph means the graph is moved left or right without changing the shape. If the graph is shifted to the right by 3 units, then the x-coordinate of each point is increased by 3.

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Vertical Compression

A vertical compression of a graph means the graph is shrunk vertically by a factor less than 1. For example, if a graph is compressed by a factor of 1/2, all its y-coordinates are halved.

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Vertical Shift

A vertical shift of a graph means the graph is moved up or down without changing the shape. If the graph is shifted up by 2 units, then the y-coordinate of each point is increased by 2.

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