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HSPT Math : HSPT Mathematics

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

Example Questions

Example Question #72 : How To Find The Solution To An Equation

Solve for :

6x + 18 = 4x + 34

Possible Answers:

The equation has no solution.

$x = 10\frac{1}{5}$

x = 26

$x = 1 \frac{3}{5}$

x = 8

Correct answer:

x = 8

Explanation:

6x + 18 = 4x + 34

6x + 18-4x = 4x + 34 -4x

6x-4x + 18 = 4x -4x+ 34

2x + 18 = 34

2x + 18 -18= 34-18

2x = 16

$2x \div 2 = 16\div 2$

x = 8

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Example Question #73 : How To Find The Solution To An Equation

Solve for .

6n+4=-8

Possible Answers:

n=1

n=-2

n=-1

n=2

Correct answer:

n=-2

Explanation:

6n+4=-8

6n+4-4=-8-4

6n=-12

$\frac{6n}{6}=\frac{-12}{6}$

n=-2

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Example Question #74 : How To Find The Solution To An Equation

Solve for :

$\frac{n+4}{2n}=\frac{7}{6}$

Possible Answers:

n=1

n=2

n=-1

n=3

Correct answer:

n=3

Explanation:

$\frac{n+4}{2n}=\frac{7}{6}$

Cross multiply:

(2n)(7)=(6)(n+4)

14n=6n+24

14n-6n=6n+24-6n

8n=24

$\frac{8n}{8}=\frac{24}{8}$

n=3

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Example Question #75 : How To Find The Solution To An Equation

Solve for .

7x-8=-15

Possible Answers:

x=-2

x=-1

x=1

x=2

Correct answer:

x=-1

Explanation:

7x-8=-15

7x-8+8=-15+8

7x=-7

$\frac{7x}{7}=\frac{-7}{7}$

x=-1

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Example Question #76 : How To Find The Solution To An Equation

Solve for :

$\frac{n-2}{n}=\frac{3}{4}$

Possible Answers:

n=4

n=8

n=6

n=3

Correct answer:

n=8

Explanation:

$\frac{n-2}{n}=\frac{3}{4}$

Cross multiply.

3n=4(n-2)

3n=4n-8

3n+8=4n-8+8

3n+8=4n

3n+8-3n=4n-3n

8=n

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Example Question #77 : How To Find The Solution To An Equation

Solve for :

6x + 8 = 3x + 44

Possible Answers:

$x = 17 \frac {1}{3}$

$x = 5 \frac{7}{9}$

x = 12

x = 4

The equation has no solution.

Correct answer:

x = 12

Explanation:

6x + 8 = 3x + 44

6x - 3x + 8= 3x - 3x + 44

(6 - 3)x + 8= 44

3x + 8= 44

3x + 8-8 = 44 -8

3x = 36

$3x \div 3= 36 \div 3$

x = 12

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Example Question #78 : How To Find The Solution To An Equation

Solve for y:

4y + 23 = 9y - 12

Possible Answers:

y = 7

The equation has no solution.

y = -7

y = 2.2

y = -2.2

Correct answer:

y = 7

Explanation:

4y + 23 = 9y - 12

4y- 4y + 23 = 9y - 4y - 12

23 = (9 - 4) y - 12

23 = 5 y - 12

23+ 12 = 5 y - 12 + 12

35 = 5 y

$35 \div 5 = 5 y \div 5$

7 = y

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Example Question #72 : How To Find The Solution To An Equation

Find the mode in this set of numbers:

412, 421, 214, 241, 142, 124, 214

Possible Answers:

142

124

214

241

Correct answer:

214

Explanation:

Find the most recurring number: 214

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Example Question #80 : How To Find The Solution To An Equation

Solve for :

6 N - 17 = 4 (N - 7)

Possible Answers:

$N = - 22 \frac{1}{2}$

$N = - 5 \frac{1}{2}$

$N = - 1 \frac{1}{10}$

N = 5

$N = - 4 \frac{1}{2}$

Correct answer:

$N = - 5 \frac{1}{2}$

Explanation:

6 N - 17 = 4 (N - 7)

$6 N - 17 = 4 \cdot N - 4 \cdot 7$

6 N - 17 = 4 N - 28

6 N - 4N - 17 = 4 N - 4N - 28

(6 -4) N - 17 = - 28

2 N - 17 = - 28

2 N - 17 + 17 = - 28+ 17

$2 N = - \left ( 28- 17 \right )$

2 N = - 11

$2 N \div 2 = - 11\div 2$

$N = - 5 \frac{1}{2}$

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Example Question #81 : How To Find The Solution To An Equation

The three angles of a triangle measure $34^{\circ }, x ^{\circ }, 3x ^{\circ }$ .

What is ?

Possible Answers:

$x= 81 \frac{1}{2} ^{\circ }$

$x= 36 \frac{1}{2} ^{\circ }$

$x = 73^{\circ }$

$x = 34 ^{\circ }$

$x= 48 \frac{2}{3} ^{\circ }$

Correct answer:

$x= 36 \frac{1}{2} ^{\circ }$

Explanation:

The measures of three angles of a triangle total $180^{\circ }$ , so set up this equation and solve:

34 + x + 3x = 180

34 + 1x + 3x = 180

$34 + \left ( 1 + 3 \right ) x = 180$

34 + 4 x = 180

34 + 4 x -34 = 180-34

4 x = 146

$4 x \div 4= 146\div 4$

$x= 36 \frac{1}{2} ^{\circ }$

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All HSPT Math Resources

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #72 : How To Find The Solution To An Equation

Example Question #73 : How To Find The Solution To An Equation

Example Question #74 : How To Find The Solution To An Equation

Example Question #75 : How To Find The Solution To An Equation

Example Question #76 : How To Find The Solution To An Equation

Example Question #77 : How To Find The Solution To An Equation

Example Question #78 : How To Find The Solution To An Equation

Example Question #72 : How To Find The Solution To An Equation

Example Question #80 : How To Find The Solution To An Equation

Example Question #81 : How To Find The Solution To An Equation

All HSPT Math Resources

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