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HSPT Math : Algebra

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Example Questions

Example Question #1754 : Hspt Mathematics

Evaluate: $-\frac{2}{z} =-8$

Possible Answers:

$\frac{1}{10}$

$\frac{1}{4}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{4}$

Explanation:

To solve this problem, isolate the variable.

Multiply by on both sides of the equation to eliminate the fraction and negative sign.

$-\frac{2}{z} \times (-z)=-8\times( -z)$

2=8z

Divide both sides by .

$z=\frac{2}{8}=\frac{1}{4}$

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Example Question #1162 : Concepts

Solve the following equation: 3x-3 = 18

Possible Answers:

Correct answer:

Explanation:

In order to isolate the unknown variable, first add three from both sides of the equation to move the negative three to the right side of the equation.

3x-3 +(3)= 18+(3)

Simplify the left and right sides.

3x=21

Divide by three on both sides.

$\frac{3x}{3}=\frac{21}{3}$

Simplify the left and right sides.

x=7

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Example Question #551 : Algebra

Solve the following for :

3x-4=11

Possible Answers:

$\frac{7}{3}$

Correct answer:

Explanation:

To solve for a particular variable, you must isolate the variable on one side of the equation and all other constants on the other side. To do this, perform the opposite operation to manipulate the equation.

To solve, you must isolate x by first adding 4 to both sides adn then dividing by 3.

Thus,

$3x-4+4=11+4\Rightarrow 3x=15\Rightarrow \frac{3x}{3}=\frac{15}{3}\Rightarrow x=5$

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Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = a^{2}+ b$

If $6 \bigstar b = 100$ , then what is ?

Possible Answers:

$\sqrt{94}$

$\sqrt{106}$

Correct answer:

Explanation:

$a \bigstar b = a^{2}+ b$ ,

$6 \bigstar b = 6 ^{2} + b = 36 + b$ .

$6 \bigstar b = 100$

then

36 + b= 100

36+ b - 36 = 100 - 36

b = 64

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Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar \frac{1}{2} = -1$ , evaluate .

Possible Answers:

$a = \frac{1}{3}$

a = -3

a = 3

$a = - \frac{1}{3}$

Correct answer:

$a = - \frac{1}{3}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$

$a \bigstar \frac{1}{2} = \frac{a+ \frac{1}{2} }{a \cdot \frac{1}{2} } = \frac{\frac{2a}{2}+ \frac{1}{2} }{ \frac{a}{2} } = \frac{\frac{2a+1}{2} }{ \frac{a}{2} }$

Equivalently

$a \bigstar \frac{1}{2} = \frac{2a+1}{2} \div \frac{a}{2} = \frac{2a+1}{2} \cdot \frac{2}{a} = \frac{2a+1}{a}$

$a \bigstar \frac{1}{2} = -1$ , so set this equal to :

$\frac{2a+1}{a} = -1$

$\frac{2a+1}{a} \cdot a = -1 \cdot a$

2a+1 = -a

2a+1 + a - 1 = -a + a - 1

3a= - 1

$3a\div 3 = - 1 \div 3$

$a = - \frac{1}{3}$

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Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar 0.5 = 0.1$ , then evaluate .

Possible Answers:

$a = \frac{ 19} {10}$

$a = - \frac{10}{19}$

$a = - \frac{ 19} {10}$

$a = \frac{10}{19}$

Correct answer:

$a = - \frac{10}{19}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$ ,

$a \bigstar 0.5 = \frac{a+0.5 }{a \cdot 0.5 } = \frac{a+0.5 }{0.5a }$

Set this equal to 0.1:

$\frac{a+0.5 }{0.5a } = 0.1$

$\frac{a+0.5 }{0.5a } \cdot 0.5 a = 0.1 \cdot 0.5 a$

a+0.5 = 0.05 a

$(a+0.5) \cdot 100 = 0.05 a \cdot 100$

$a \cdot 100 +0.5 \cdot 100 = 5 a$

100a +5 0= 5 a

100a +50 - 100a = 5 a - 100a

50 = -95a

$50 \div (-95) = -95a \div (-95)$

$a = -\frac{50}{95} = - \frac{10}{19}$

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Example Question #1166 : Concepts

is a number less than 36.

Which of the following gives a solution of the equation

|x- 17 | + K = 36

in terms of ?

Possible Answers:

x = -53 - K

x = 19 - K

x = 53 - K

x = -19 - K

Correct answer:

x = 53 - K

Explanation:

|x- 17 | + K = 36 ,

|x- 17 | + K - K = 36 - K

|x- 17 | = 36 - K

Since K < 36 , 36 - K > 0 , so solutions exist. One of the following two situations occurs:

x- 17 = 36 - K

x- 17 + 17 = 36 - K + 17

x = 53 - K

-(x- 17 )= 36 - K

-x+ 17 = 36 - K

-x+ 17 - 17 = 36 - K - 17

-x = 19 - K

-(-x )= -(19 - K)

x = K - 19

Of these two, only x = 53 - K is among the choices, so it is the correct choice.

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Example Question #1164 : Concepts

If L < 32 , then which of the following is equivalent to the expression | L - 32 | + 12 ?

Possible Answers:

20+L

44 + L

44 - L

20-L

Correct answer:

44 - L

Explanation:

If L < 32 , then L - 32 < 0 , so

| L - 32 | + 12

= -(L - 32 )+ 12

= - L + 32 + 12

= - L + 44

= 44 - L

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Example Question #552 : Algebra

If L > 47 , then which of the following is equivalent to the expression | L - 47 | - 32 ?

Possible Answers:

L - 79

L - 15

- L + 79

- L + 15

Correct answer:

L - 79

Explanation:

If L > 47 , then L - 47 > 0 , so

| L - 47 | - 32

= L - 47 - 32

= L - 79

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Example Question #1761 : Hspt Mathematics

If 4< X< 12 , then

|X - 12| + |X- 4|

can be rewritten as which of the following?

Possible Answers:

2X-16

-2X + 16

Correct answer:

Explanation:

If X > 4 , then

X - 4 >0 , so

|X- 4| = X-4 .

If X< 12 , then

X - 12 < 0 , so

|X- 12| = -(X-12)= -X + 12

|X - 12| + |X- 4|

= X-4 + (-X + 12)

= X-X -4 + 12

= 8

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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1754 : Hspt Mathematics

Example Question #1162 : Concepts

Example Question #551 : Algebra

Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #1166 : Concepts

Example Question #1164 : Concepts

Example Question #552 : Algebra

Example Question #1761 : Hspt Mathematics

All HSPT Math Resources

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