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Algebra Chapter Inequalities and Absolute Values

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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?

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

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

$n$ does not produce a valid solution Signup and view all the answers

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

a < -1.75 or a > 1 Signup and view all the answers

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

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

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

Absolute value cannot be less than or equal to a negative number. Signup and view all the answers

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

(-28, 4) 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?

The values of a where the inequality holds true. Signup and view all the answers