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Algebra

SAT Absolute Value

         

Which of the following is the value of \(-10 \cdot \Bigg| - \Big|- \big| -12 \big| \Big| \Bigg| \)?

(A) \(\ \ -120\)
(B) \(\ \ -2\)
(C) \(\ \ -10\)
(D) \(\ \ 22\)
(E) \(\ \ 120\)

If \(x>y>0\), which of the following equals \(|7x-6y|+|6y-7x|\)?

(A) \(\ \ 0\)
(B) \(\ \ xy\)
(C) \(\ \ x-y\)
(D) \(\ \ 14x-12y\)
(E) \(\ \ 14x+12y\)

\(|-13x+6|=7\)
\(|11y|=66\)

The coordinates of point \(P\) are determined by the equations above. If \(P\) lies in the fourth quadrant, what are its coordinates?

(A) \(\ \ (-6, 6)\)

(B) \(\ \ (-\frac{1}{13}, -6)\)

(C) \(\ \ (-\frac{1}{13}, 1)\)

(D) \(\ \ (1, -6)\)

(E) \(\ \ (6, -\frac{1}{13})\)

Which of the following is equivalent to \(|16x+7|>8\)?

(A) \(\ \ x<-\frac{15}{16} \)

(B) \(\ \ x<-\frac{15}{16} \) or \(x>\frac{1}{16}\)

(C) \(\ \ -\frac{15}{16} < x < \frac{1}{16}\)

(D) \(\ \ x=\frac{1}{16}\)

(E) \(\ \ x>\frac{1}{16}\)

\[\begin{array}{r c l} 4|s-1|&=&8\\ \\ \frac{|t+2|}{2}&=&9 \end{array}\]

Which of the following CANNOT equal \(|s-t|\)?

(A) \(\ \ 13\)
(B) \(\ \ 17\)
(C) \(\ \ 19\)
(D) \(\ \ 23\)
(E) \(\ \ 26\)

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