C 957 | C957 Exam 1: Applied Algebra Updated and
Latest Questions and Correct Answers with
Rationale - WGU
1. What is the value of the expression 15 - 3 * (2 + 4) / 2?
A. 36
B. 6
C. 9
D. 12
Correct Answer: B
Explanation: First, evaluate the expression inside the parentheses which is 2 plus 4 equals
6. Next, multiply 3 by 6 to get 18 following the multiplication rule. Then, divide 18 by 2
which results in 9. Finally, subtract 9 from 15 to find the final value of 6. This sequence
strictly follows the order of operations known as PEMDAS.
2. Which of the following numbers is considered an irrational number?
A. 0.75
B. sqrt(2)
C. -5
D. 2/3
Correct Answer: B
Explanation: An irrational number cannot be expressed as a simple fraction of two
integers. The square root of 2 results in a non-repeating and non-terminating decimal.
Values like 0.75 and 2/3 are rational because they can be written as fractions. Integers like
-5 are also rational because they can be written over one. Therefore, the square root of 2 is
the only irrational choice.
3. Simplify the following algebraic expression: 4(x - 3) + 2x + 5.
A. 6x + 2
B. 6x - 7
C. 4x - 7
D. 6x - 12
Correct Answer: B
,Explanation: Begin by distributing the 4 to both terms inside the parentheses to get 4x
minus 12. Next, list all the terms in the expression which are 4x, -12, 2x, and 5. Combine the
like terms 4x and 2x to obtain 6x. Then, combine the constants -12 and 5 to get -7. The fully
simplified expression is 6x minus 7.
4. Solve the linear equation for x: 3x + 7 = 22.
A. x = 9
B. x = 3
C. x = 5
D. x = 15
Correct Answer: C
Explanation: To solve for x, you must first isolate the variable term by subtracting 7 from
both sides. This subtraction results in the equation 3x equals 15. Next, divide both sides of
the equation by 3 to solve for x. The calculation of 15 divided by 3 gives a result of 5. You
can verify this by plugging 5 back into the original equation.
5. If x = -4, what is the value of the expression x^2 + 2x - 1?
A. 9
B. 23
C. -25
D. 7
Correct Answer: D
Explanation: Start by substituting -4 for every instance of x in the expression. Square -4 to
get 16, noting that a negative times a negative is positive. Multiply 2 by -4 to get -8 for the
middle term. Now combine the results: 16 plus -8 minus 1. This simplifies to 8 minus 1,
resulting in a final answer of 7.
6. Which expression represents ‘five less than double a number n’?
A. 5 - 2n
B. 2n - 5
C. 2(n - 5)
D. n/2 - 5
Correct Answer: B
Explanation: The phrase ‘double a number’ is mathematically translated to 2 multiplied by
n. ‘Five less than’ indicates that 5 should be subtracted from that product. Therefore, the
, subtraction of 5 must occur after the doubling of n. Option A incorrectly reverses the order
of subtraction. Option B correctly identifies the relationship as 2n minus 5.
7. Solve the equation: 2(x + 5) = 3x - 4.
A. x = 1
B. x = 9
C. x = 6
D. x = 14
Correct Answer: D
Explanation: First, use the distributive property to expand the left side to 2x plus 10. Next,
subtract 2x from both sides to move all variable terms to one side. This leaves the equation
10 equals x minus 4. Add 4 to both sides to isolate the variable x. The final result is x equals
14, which satisfies the equality.
8. What is the multiplicative inverse of -3/4?
A. -4/3
B. 3/4
C. 4/3
D. 1
Correct Answer: A
Explanation: The multiplicative inverse of a number is what you multiply it by to get 1. To
find the inverse of a fraction, you simply flip the numerator and denominator. The sign of
the number must remain the same to yield a positive product. Flipping -3/4 gives -4/3.
Multiplying -3/4 by -4/3 results in 1, confirming the answer.
9. Simplify the expression: -(3x - 8) + 4x.
A. x - 8
B. 7x - 8
C. -3x + 12
D. x + 8
Correct Answer: D
Explanation: The negative sign outside the parentheses must be distributed to both terms
inside. This changes 3x to -3x and -8 to positive 8. Now the expression is -3x plus 8 plus 4x.
Combine the like terms -3x and 4x to get 1x or simply x. The remaining constant is 8,
leading to the final result of x plus 8.
Latest Questions and Correct Answers with
Rationale - WGU
1. What is the value of the expression 15 - 3 * (2 + 4) / 2?
A. 36
B. 6
C. 9
D. 12
Correct Answer: B
Explanation: First, evaluate the expression inside the parentheses which is 2 plus 4 equals
6. Next, multiply 3 by 6 to get 18 following the multiplication rule. Then, divide 18 by 2
which results in 9. Finally, subtract 9 from 15 to find the final value of 6. This sequence
strictly follows the order of operations known as PEMDAS.
2. Which of the following numbers is considered an irrational number?
A. 0.75
B. sqrt(2)
C. -5
D. 2/3
Correct Answer: B
Explanation: An irrational number cannot be expressed as a simple fraction of two
integers. The square root of 2 results in a non-repeating and non-terminating decimal.
Values like 0.75 and 2/3 are rational because they can be written as fractions. Integers like
-5 are also rational because they can be written over one. Therefore, the square root of 2 is
the only irrational choice.
3. Simplify the following algebraic expression: 4(x - 3) + 2x + 5.
A. 6x + 2
B. 6x - 7
C. 4x - 7
D. 6x - 12
Correct Answer: B
,Explanation: Begin by distributing the 4 to both terms inside the parentheses to get 4x
minus 12. Next, list all the terms in the expression which are 4x, -12, 2x, and 5. Combine the
like terms 4x and 2x to obtain 6x. Then, combine the constants -12 and 5 to get -7. The fully
simplified expression is 6x minus 7.
4. Solve the linear equation for x: 3x + 7 = 22.
A. x = 9
B. x = 3
C. x = 5
D. x = 15
Correct Answer: C
Explanation: To solve for x, you must first isolate the variable term by subtracting 7 from
both sides. This subtraction results in the equation 3x equals 15. Next, divide both sides of
the equation by 3 to solve for x. The calculation of 15 divided by 3 gives a result of 5. You
can verify this by plugging 5 back into the original equation.
5. If x = -4, what is the value of the expression x^2 + 2x - 1?
A. 9
B. 23
C. -25
D. 7
Correct Answer: D
Explanation: Start by substituting -4 for every instance of x in the expression. Square -4 to
get 16, noting that a negative times a negative is positive. Multiply 2 by -4 to get -8 for the
middle term. Now combine the results: 16 plus -8 minus 1. This simplifies to 8 minus 1,
resulting in a final answer of 7.
6. Which expression represents ‘five less than double a number n’?
A. 5 - 2n
B. 2n - 5
C. 2(n - 5)
D. n/2 - 5
Correct Answer: B
Explanation: The phrase ‘double a number’ is mathematically translated to 2 multiplied by
n. ‘Five less than’ indicates that 5 should be subtracted from that product. Therefore, the
, subtraction of 5 must occur after the doubling of n. Option A incorrectly reverses the order
of subtraction. Option B correctly identifies the relationship as 2n minus 5.
7. Solve the equation: 2(x + 5) = 3x - 4.
A. x = 1
B. x = 9
C. x = 6
D. x = 14
Correct Answer: D
Explanation: First, use the distributive property to expand the left side to 2x plus 10. Next,
subtract 2x from both sides to move all variable terms to one side. This leaves the equation
10 equals x minus 4. Add 4 to both sides to isolate the variable x. The final result is x equals
14, which satisfies the equality.
8. What is the multiplicative inverse of -3/4?
A. -4/3
B. 3/4
C. 4/3
D. 1
Correct Answer: A
Explanation: The multiplicative inverse of a number is what you multiply it by to get 1. To
find the inverse of a fraction, you simply flip the numerator and denominator. The sign of
the number must remain the same to yield a positive product. Flipping -3/4 gives -4/3.
Multiplying -3/4 by -4/3 results in 1, confirming the answer.
9. Simplify the expression: -(3x - 8) + 4x.
A. x - 8
B. 7x - 8
C. -3x + 12
D. x + 8
Correct Answer: D
Explanation: The negative sign outside the parentheses must be distributed to both terms
inside. This changes 3x to -3x and -8 to positive 8. Now the expression is -3x plus 8 plus 4x.
Combine the like terms -3x and 4x to get 1x or simply x. The remaining constant is 8,
leading to the final result of x plus 8.
