5.11: Proficiency Exam
Proficiency Exam
Solve the equations and inequalities for the following problems.
\(x+8=14\)
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\(x=6\)
\(6a+3=−10\)
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\(a = \dfrac{-13}{6}\)
\(\dfrac{-3a}{8} = 6\)
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\(a=−16\)
\(\dfrac{x}{-2} + 16 = 11\)
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\(x=10\)
\(\dfrac{y-9}{4} + 6 = 3\)
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\(y=−3\)
\(5b−8=7b+12\)
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\(b=−10\)
\(3(2a+4)=2(a+3)\)
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\(a = -\dfrac{3}{2}\)
\(5(y+3)−(2y−1)=−5\)
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\(y=−7\)
\(\dfrac{-(4x+3-5x)}{3} = 2\)
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\(x=9\)
Solve \(2p−6q+1=−2\) for \(p\).
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\(p = \dfrac{6q-3}{2}\)
Solve \(p = \dfrac{nRT}{V}\) for \(T\)
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\(T = \dfrac{Vp}{nR}\)
\(a−8≥4\)
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\(a≥12\)
\(−3a+1<−5\)
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\(a>2\)
\(−2(a+6)≤−a+11\)
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\(a≥−23\)
\(\dfrac{-4x-3}{3} > -9\)
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\(x<6\)
Translate the phrases or sentences into mathematical expressions or equations for the following problems.
Three added to twice a number.
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\(3+2a\)
Eight less than two thirds of a number.
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\(\dfrac{2}{3}x - 8\)
Two more than four times a number.
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\(2+4x\)
A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.
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\(2x(x^3) = 12\)
A number is decreased by five and that result is divided by ten more than the original number. The result is six times the original number.
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\(\dfrac{x-5}{x+10} = 6x\)
Solve the following problems.
Eight percent of a number is 1.2. What is the number?
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\(x=15\)
Three consecutive odd integers sum to 38. What are they?
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There are no three consecutive odd integers that add to 38.
Five more than three times a number is strictly less than seventeen. What is the number?
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\(x<4\)
Solve \(y=8x−11\) for \(y\) if \(x=3\), and write the solution as an ordered pair.
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\((3,13)\)