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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #291 : Algebra

Solve for :

$- \frac{6}{5}y > -\frac{9}{20}$

Possible Answers:

$y> - \frac{3}{8}$

$y> \frac{3}{8}$

$y< - \frac{3}{8}$

$y< \frac{3}{8}$

Correct answer:

$y< \frac{3}{8}$

Explanation:

$- \frac{6}{5}y > -\frac{9}{20}$

$- \frac{5}{6} \left ( - \frac{6}{5} y \right )< - \frac{5}{6} \left ( -\frac{9}{20} \right )$

Note: switch the symbol when dividing by a negative number

$y< \frac{5}{6} \cdot \frac{9}{20}$

$y< \frac{1}{2} \cdot \frac{3}{4}$

$y< \frac{3}{8}$

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Example Question #98 : How To Find The Solution To An Equation

Solve for :

6 (t - 0.13 ) = 9

Possible Answers:

t = 1.63

t = 1.37

t = 1.47

t = 1.52

Correct answer:

t = 1.63

Explanation:

Distribute, then solve:

6 (t - 0.13 ) = 9

$6 \cdot t - 6 \cdot 0.13 = 9$

6 t - 0.78 = 9

6 t - 0.78 + 0.78 = 9+ 0.78

6 t = 9.78

$6 t \div 6 = 9.78 \div 6$

t = 1.63

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Example Question #901 : Concepts

Solve for :

10 - 0.4t = 8.11

Possible Answers:

t = 4.725

t = 45.275

t = -4.725

t = - 45.275

Correct answer:

t = 4.725

Explanation:

10 - 0.4t = 8.11

10 - 0.4t - 10 = 8.11- 10

-0.4t = - ( 10.00 - 8.11 )

-0.4t = - 1.89

$0.4t \div 0.4 = - 1.89 \div \left ( -0.4 \right )$

$t = 1.89 \div 0.4$

Move each decimal point one digit right:

$t = 18.9 \div 4 = 4.725$

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Example Question #101 : Equations

Give the solution set of the inequality:

4t + 9 < 35

Possible Answers:

t < 11

$t < 6 \frac{1}{2}$

t < 13

$t < 7 \frac{1}{2}$

Correct answer:

$t < 6 \frac{1}{2}$

Explanation:

4t + 9 < 35

4t + 9 -9 < 35-9

4t < 26

$4t \div 4 < 26 \div 4$

$t < 6 \frac{2}{4}$

$t < 6 \frac{1}{2}$

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Example Question #301 : Algebraic Concepts

f(x) = 50 - 4x

Evaluate f (10.5 )

Possible Answers:

Correct answer:

Explanation:

f(x) = 50 - 4x

$f(10.5) = 50 - 4 \cdot 10.5 = 50 - 42 = 8$

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Example Question #101 : How To Find The Solution To An Equation

Define $f (x) = \frac{1}{2} x - 7$

Evaluate: f (12)

Possible Answers:

$2 \frac{1}{2}$

$6 \frac{1}{2}$

Correct answer:

Explanation:

$f (x) = \frac{1}{2} x - 7$

$f (12) = \frac{1}{2} \cdot 12 - 7$

f (12) =6- 7

f (12) =-1

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Example Question #104 : Equations

Define $g (x) =\left ( x -6 \right )^{2}$

Evaluate g(8.7)

Possible Answers:

13.69

9.61

7.29

2.89

Correct answer:

7.29

Explanation:

$g (x) =\left ( x -6 \right )^{2}$

$g (8.7 ) =\left (8.7 -6 \right )^{2}$

$g (8.7 ) =2.7 ^{2}$

$g (8.7 ) =2.7 \cdot 2.7$

g (8.7 ) =7.29

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Example Question #105 : Equations

Solve for :

0.7t + 0.23 = 0.3 t - 3.21

Possible Answers:

t = - 3.44

t = -7.45

t = - 8.6

t = -2.98

Correct answer:

t = - 8.6

Explanation:

0.7t + 0.23 = 0.3 t - 3.21

0.7t + 0.23 - 0.3t = 0.3 t - 3.21 - 0.3t

0.4t + 0.23 = - 3.21

0.4t + 0.23- 0.23 = - 3.21 - 0.23

0.4t = - 3.44

$0.4t \div 0.4 = - 3.44 \div 0.4$

$t = - 3.44 \div 0.4$

Move each decimal point one digit right:

$t = - 34.4 \div 4 = - 8.6$

Report an Error

Example Question #106 : Equations

Solve for :

4 t - 1.9 = 8.3

Possible Answers:

t = 2.55

t = 0.16

t = 1.6

t = 0.255

Correct answer:

t = 2.55

Explanation:

4 t - 1.9 = 8.3

4 t - 1.9 + 1.9 = 8.3 + 1.9

4 t = 10.2

$4 t \div 4= 10.2 \div 4$

t = 2.55

Report an Error

Example Question #107 : Equations

Solve for :

$\frac{4}{5} d > - \frac{7}{10}$

Possible Answers:

$d > - \frac{7}{8}$

$d > - \frac{14}{25}$

$d < - \frac{7}{8}$

$d < - \frac{14}{25}$

Correct answer:

$d > - \frac{7}{8}$

Explanation:

$\frac{4}{5} d > - \frac{7}{10}$

$\frac{5}{4} \cdot \frac{4}{5} d >\frac{5}{4} \cdot \left ( - \frac{7}{10} \right )$

$d > - \left (\frac{5}{4} \cdot \frac{7}{10} \right )$

$d > - \left (\frac{1}{4} \cdot \frac{7}{2} \right )$

$d > - \frac{7}{8}$

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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #291 : Algebra

Example Question #98 : How To Find The Solution To An Equation

Example Question #901 : Concepts

Example Question #101 : Equations

Example Question #301 : Algebraic Concepts

Example Question #101 : How To Find The Solution To An Equation

Example Question #104 : Equations

Example Question #105 : Equations

Example Question #106 : Equations

Example Question #107 : Equations

All HSPT Math Resources

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