Intermediate Algebra Chapter 1

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Quizzes Created: 3 | Total Attempts: 671
Questions: 27 | Attempts: 291

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Fractions Exponents,
Order of Operations
Inequality Variables Expressions, and Equations
Real Numbers and the Number Line Adding and Subtracting Real Numbers Multiplying and Dividing Real Numbers Properties of Real Numbers Simplifying Expressions

• 1.

Write in lowest terms:

Explanation
The given question asks to write the fraction 7/11 in its lowest terms. The fraction 7/11 is already in its lowest terms, as there are no common factors that can be divided from both the numerator (7) and the denominator (11). Therefore, the fraction 7/11 cannot be simplified any further.

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• 2.

Explanation
The given expression is 241/120. This is the simplest form of the fraction and cannot be further simplified. The numerator (241) is a prime number and the denominator (120) can be divided by 2 to get 60, and then by 2 again to get 30. Since there are no common factors between the numerator and denominator, the fraction is already in its simplest form. Therefore, the answer is 241/120.

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• 3.

Divide

Explanation
When dividing two numbers, the answer is obtained by dividing the numerator of the first number by the numerator of the second number and dividing the denominator of the first number by the denominator of the second number. In this case, dividing 19 by 18 gives the answer 19/18.

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• 4.

Decide whether 4[-20+7(-1)] 135

• A.

True

• B.

False

A. True
Explanation
The given expression can be simplified as follows: 4[-20+7(-1)] = 4[-20-7] = 4[-27]. Multiplying -27 by 4 gives -108. Since -108 is less than 135, the statement 4[-20+7(-1)] < 135 is true.

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• 5.

Graph the group of numbers -1, -3,1-41,1-11 on a number line.

-4 -2 0 2 4
Explanation
The given numbers are -1, -3, -41, and -11. When we graph these numbers on a number line, we place them at their respective positions. -1 is to the left of 0, -3 is further to the left, -41 is even further to the left, and -11 is between -3 and -41. Therefore, the graphed numbers on the number line would be -41, -11, -3, -1, 0, 2, 4.

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• 6.

To which of the following sets does   belong: natural numbers whole numbers mtegers rational numbers irrational numbers real numbers?

rational numbers, real numbers
Explanation
The number in question belongs to the set of rational numbers because it can be expressed as a fraction of two integers. Additionally, it belongs to the set of real numbers because it can be plotted on the number line and is not imaginary.

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• 7.

-2-(5-17)+(-6)

4
Explanation
The given expression is -2-(5-17)+(-6). To simplify the expression, we start by evaluating the innermost parentheses, which is (5-17). Subtracting 17 from 5 gives us -12. The expression now becomes -2-(-12)+(-6). Since we have a negative sign in front of the parentheses, we can rewrite it as -2+12+(-6). Next, we add the numbers together, giving us 4. Therefore, the answer is 4.

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• 8.

Question No Image

-17/6
Explanation
The given expression is -17/6. This means that the numerator is -17 and the denominator is 6. The negative sign indicates that the fraction is negative. Therefore, the correct answer is -17/6.

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• 9.

-6-[-7+(2-3)]

2
Explanation
The given expression involves subtraction, addition, and multiplication. First, we simplify the expression inside the parentheses: -7+(2-3) = -7+(-1) = -8. Then, we multiply -6 by -8: -6 * -8 = 48. Finally, we divide 48 by 2, resulting in the answer 24. Therefore, the correct answer is 24.

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• 10.

6
• 11.

108
• 12.

-7 -(6+2) / -5 - (-4)

3
Explanation
The given expression involves a combination of addition, subtraction, and division operations. To simplify the expression, we first perform the operations inside the parentheses: (6+2) = 8 and -(-4) = 4. Then, we simplify the expression further: -7 - 8 / -5 - 4. Next, we perform the division operation: 8 / -5 = -1.6. Finally, we combine the remaining terms: -7 - (-1.6) - 4 = -7 + 1.6 - 4 = -9.4. Therefore, the correct answer is -9.4, not 3.

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• 13.

30(-1-2) / -9[3-(-2)]-12(-2)

30/7
Explanation
The given expression involves multiplication, division, and subtraction operations. By simplifying the expression according to the order of operations, we first evaluate the expressions within parentheses, then perform the subtraction, and finally the division. After simplifying the expression, we get the result of 30/7.

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• 14.

Find the solution of each equation from the set { - 6, -4, -2,0,2,4, 6} by guessing or by trial and error. -x + 3 = -3

6
Explanation
The equation -x + 3 = -3 can be solved by substituting each value from the given set into the equation and checking if it satisfies the equation. By guessing or trial and error, it is found that when x is equal to 6, the equation becomes -6 + 3 = -3, which is true. Therefore, the solution to the equation is x = 6.

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• 15.

Find the solution of each equation from the set { -6, -4, - 2,0,2,4, 6} by guessing or by trial and error. -3x = -12

4
Explanation
The given equation is -3x = -12. To find the solution, we need to determine the value of x. By trial and error, we can substitute each value from the set { -6, -4, -2, 0, 2, 4, 6} into the equation and check if it satisfies the equation. After trying all the values, we find that when x = 4, the equation is satisfied. Therefore, the solution to the equation -3x = -12 is x = 4.

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• 16.

Evaluate each expression given x = -2 and y = 4.

-70
Explanation
When evaluating the expression, we substitute the values of x and y into the expression. In this case, x = -2 and y = 4. Plugging these values into the expression, we get -70. Therefore, the answer to the expression when x = -2 and y = 4 is -70.

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• 17.

5x + 7y / 3(x + y)

3
Explanation
The given expression is a fraction with a numerator of 5x + 7y and a denominator of 3(x + y). To simplify the expression, we can divide each term in the numerator by the denominator. This results in 5x + 7y divided by 3(x + y). Since there are no like terms in the numerator and denominator, we cannot simplify the expression any further. Therefore, the answer is 3.

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• 18.

The highest elevation in Argentina is Mt. Aconcagua, which is 6960 m above sea level. The lowest point in Argentina is the Valdes Peninsula, 40 m below sea level. Find the difference between the highest and lowest elevations.

7000 m
Explanation
The difference between the highest and lowest elevations in Argentina can be found by subtracting the lowest point (40 m below sea level) from the highest point (6960 m above sea level). This calculation gives us a difference of 7000 m.

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• 19.

For a certain system of rating relief pitchers, 3 points are awarded for a save, 3 points are awarded for a win, 2 points are subtracted for a loss, and 2 points are subtracted for a blown save. If Mariano Rivera of the New York Yankees has 4 saves, 3 wins, 2 losses, and 1 blown save, how many points does he have?

15
Explanation
In this system of rating relief pitchers, 3 points are awarded for a save and 3 points are awarded for a win. Mariano Rivera has 4 saves and 3 wins, so he would receive a total of 4*3 + 3*3 = 12 points for these achievements. Additionally, 2 points are subtracted for a loss and 2 points are subtracted for a blown save. Rivera has 2 losses and 1 blown save, so a total of 2*2 + 1*2 = 6 points would be subtracted. Therefore, his total points would be 12 - 6 = 6 points.

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• 20.

(5 + 2) + 8 = 8 + (5 + 2)

• A.

Commutative property

• B.

Associative property

• C.

Inverse property

• D.

Identity property

• E.

Distributive property

A. Commutative property
Explanation
The given equation (5 + 2) + 8 = 8 + (5 + 2) demonstrates the commutative property. The commutative property states that the order of the numbers being added or multiplied does not affect the result. In this case, both sides of the equation have the same numbers being added, but in a different order. However, the result is the same, which confirms the commutative property.

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• 21.

-5 + (3 + 2) = (-5 + 3) + 2

• A.

Commutative property

• B.

Identity property

• C.

Distributive property

• D.

Associative property

D. Associative property
Explanation
The given equation shows the addition of two numbers (-5 and (3 + 2)). According to the associative property of addition, the grouping of numbers being added does not affect the sum. In this case, the numbers can be grouped as (-5 + 3) + 2 or -5 + (3 + 2), and the sum will be the same. Therefore, the correct answer is the associative property.

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• 22.

Question No Image

• A.

Distributive property

• B.

Inverse property

• C.

Commutative property

• D.

Inverse property

D. Inverse property
Explanation
The given answer is "inverse property." This property states that for any real number a, there exists an additive inverse -a such that a + (-a) = 0. This property is also known as the additive inverse property, as it deals with the addition of numbers and the existence of their additive inverses.

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• 23.

3x + 0 = 3x

• A.

Commutative property

• B.

Identity property

• C.

Inverse property

• D.

Distributive property

B. Identity property
Explanation
The given equation is 3x + 0 = 3x. In this equation, the addition of 0 does not change the value of 3x. This property is known as the identity property of addition, which states that adding 0 to any number does not change its value. Therefore, the correct answer is the identity property.

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• 24.

-3(x + y) = -3x + (-3y)

• A.

Inverse property

• B.

Associative property

• C.

Identity property

• D.

Distributive property

D. Distributive property
Explanation
The given equation -3(x + y) = -3x + (-3y) demonstrates the distributive property. This property states that when multiplying a number by a sum or difference of numbers, the result is the same as multiplying the number by each term in the sum or difference and then adding or subtracting the products. In this case, -3 is being multiplied by the sum (x + y), and according to the distributive property, it can be distributed to each term within the parentheses, resulting in -3x + (-3y).

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• 25.

What property is used to show that 3(x + 1) = 3x + 3?

Distributive property
Explanation
The distributive property is used to show that 3(x + 1) = 3x + 3. This property states that when a number is multiplied by a sum, it can be distributed to each term within the parentheses. In this case, the 3 is distributed to both the x and the 1, resulting in 3x + 3.

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• 26.

Simplify by combining like terms. 8x + 4x - 6x + x + 14x

21x
Explanation
The given expression involves terms with the variable x. To simplify the expression, we can combine the like terms by adding or subtracting their coefficients. In this case, we have 8x, 4x, -6x, x, and 14x. By adding the coefficients of the like terms, we get 8x + 4x - 6x + x + 14x = 21x. Therefore, the simplified expression is 21x.

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• 27.

Simplify by combining like terms. 5(2x -1) - (x-12) + 2(3x - 5)

15 x -3
Explanation
The given expression involves simplifying by combining like terms. We start by distributing the 5 to the terms inside the parentheses, resulting in 10x - 5. Then, we distribute the 2 to the terms inside the second set of parentheses, resulting in 6x - 10. Finally, we combine like terms by adding the x terms together, resulting in 16x, and adding the constant terms together, resulting in -15. Therefore, the simplified expression is 16x - 15.

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• Current Version
• Aug 09, 2024
Quiz Edited by
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• Jun 10, 2012
Quiz Created by
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