Question 1

Write the sentence as an equation. Let the variable x represent the number.
-The sum of twice a number and 5 is 11.
A) x + 10 = 11
B) 10x = 11
C) 2x + 5 = 11
D) 2x - 5 = 11

Accepted Answer

The sentence "The sum of twice a number and 5 is 11" translates to the equation 2x + 5 = 11, where x represents the number.

Question 2

Write the sentence as an equation. Let the variable x represent the number.
-Four times a number is 24.
A) 4x = 24
B) x + 4 = 24
C) x - 4 = 24
D) $\frac { 4 } { x } = 24$

Accepted Answer

The sentence "Four times a number is 24" translates to the mathematical equation 4x = 24, where x is the variable representing the number.

Question 3

Write the English phrase as an algebraic expression. Let the variable x represent the number.
-the sum of 40 divided by a number and that number divided by 40
A) $\frac { 40 + x } { 40 }$
B) $\frac { 40 } { x } - \frac { x } { 40 }$
C) $\frac { 40 } { x } + \frac { x } { 40 }$
D) $\frac { 40 + x } { x + 40 }$

Accepted Answer

The phrase "the sum of 40 divided by a number and that number divided by 40" translates to adding together two fractions: one with 40 in the numerator and the variable in the denominator, and the other with the variable in the numerator and 40 in the denominator, which is represented by option C: $\frac { 40 } { x } + \frac { x } { 40 }$.

Question 4

Write the sentence as an equation. Let the variable x represent the number.
-Four times a number is equal to 25 decreased by the number.
A) 4 + x = 25 - x
B) 4x = 25 - x
C) 4x = x - 25
D) 4x = 25 + x

Accepted Answer

The correct equation that represents "Four times a number is equal to 25 decreased by the number" is 4x = 25 - x, where x is the number.

Question 5

Write the sentence as an equation. Let the variable x represent the number.
-The product of 6 and a number, increased by 2, is 32.
A) 12x = 32
B) 6x + 2 = 32
C) 6x - 2 = 32
D) 6(x + 2) = 32

Accepted Answer

The correct representation is "6x + 2 = 32" because it translates to "the product of 6 and a number (6x), increased by 2, equals 32."

Question 6

Write the sentence as an equation. Let the variable x represent the number.
-The quotient of 15 and a number is $\frac { 1 } { 4 }$.
A) $\frac { 15 } { x } = \frac { 1 } { 4 }$
B) $15 x = \frac { 1 } { 4 }$
C) $\frac { x } { 15 } = \frac { 1 } { 4 }$
D) $x + 15 = \frac { 1 } { 4 }$

Accepted Answer

The quotient of 15 and a number (x) is expressed as $\frac{15}{x}$, which equals $\frac{1}{4}$, matching option A.

Question 7

Determine if the given value is a solution to the equation.
-3a + 2 = 2a + 5; 3
A) solution
B) not a solution

Accepted Answer

When substituting $a = 3$ into the equation, it becomes $3(3) + 2 = 2(3) + 5$, which simplifies to $9 + 2 = 6 + 5$, or $11 = 11$, proving that $a = 3$ is indeed a solution.

Question 8

Write the sentence as an equation. Let the variable x represent the number.
-Seven less than 4 times a number gives 5.
A) 7 - 4x = 5
B) $\frac { 4 x } { 7 } = 5$
C) x - 28 = 5
D) 4x - 7 = 5

Accepted Answer

The correct translation of "Seven less than 4 times a number gives 5" is "4x - 7 = 5". This means you take four times a number (4x) and subtract 7 from it to get 5.

Question 9

Determine if the given value is a solution to the equation.
-3(w + 2) = 4(w - 1); 9
A) solution
B) not a solution

Accepted Answer

Substituting 9 for w in the equation 3(w + 2) = 4(w - 1) gives 3(11) = 4(8), which simplifies to 33 ≠ 32, indicating that 9 is not a solution.

Question 10

Determine if the given value is a solution to the equation.
-$\frac { r } { 4 } = 5 ; 15$
A) solution
B) not a solution

Accepted Answer

To determine if 15 is a solution, substitute $r$ with 15 in the equation: $\frac{15}{4} = 5$. This simplifies to $3.75 = 5$, which is false. Therefore, 15 is not a solution to the equation.

Question 11

Determine if the given value is a solution to the equation.
-y - 2 = 1; 3
A) solution
B) not a solution

Accepted Answer

y - 2 = 13 - 2 = 11 = 1The equation is true, so 3 is a solution.

Question 12

Determine if the given value is a solution to the equation.
-3z = 18; 6
A) not a solution
B) solution

Accepted Answer

When you substitute z = 6 into the equation 3z = 18, it satisfies the equation because 3(6) = 18.

Question 13

Write the sentence as an equation. Let the variable x represent the number.
-The difference between 50 and a number is 10.
A) 50 + x = 10
B) 50 - x = 10
C) $\frac { 50 } { x } = 10$
D) x - 50 = 10

Accepted Answer

The correct equation that represents "The difference between 50 and a number is 10" is 50 - x = 10, as it directly translates the words into a mathematical expression.

Question 14

Determine if the given value is a solution to the equation.
-60 - y = 10; 60
A) solution
B) not a solution

Accepted Answer

Substituting y = 60 into the equation 60 - y = 10 gives 60 - 60 = 0, which is not equal to 10. Therefore, 60 is not a solution.

Question 15

Determine if the given value is a solution to the equation.
-$4 ( p - 1 ) = 2 p ; 2$
A) not a solution
B) solution

Accepted Answer

To determine if $2$ is a solution to the equation $4(p - 1) = 2p$, substitute $p = 2$ into the equation: $4(2 - 1) = 2(2)$. This simplifies to $4 = 4$, which is true. Therefore, $2$ is a solution to the equation.

Question 16

Determine if the given value is a solution to the equation.
-4m + 8 = 42; 8
A) not a solution
B) solution

Accepted Answer

Substituting $m = 8$ into the equation $4m + 8 = 42$ gives $4(8) + 8 = 32 + 8 = 40$, which is not equal to 42, so $m = 8$ is not a solution.

Question 17

Write the sentence as an equation. Let the variable x represent the number.
-Find the perimeter of a rectangle if the length, L, is 8 meters and the width, W, is 7 meters. Use the formula P = 2L + 2W.
A) 112 m
B) 23 m
C) 30 m
D) 15 m

Accepted Answer

The perimeter of a rectangle is calculated using the formula P = 2L + 2W. Substituting L = 8 meters and W = 7 meters gives P = 2(8) + 2(7) = 16 + 14 = 30 meters.

Question 18

Write the English phrase as an algebraic expression. Let the variable x represent the number.
-one more than the quotient of a number and 45
A) $45 x - 1$
B) $\frac { 45 } { x } + 1$
C) $45 x + 1$
D) $\frac { x } { 45 } + 1$

Accepted Answer

The phrase "one more than the quotient of a number and 45" translates to adding 1 to the result of dividing a number by 45, which is represented as $\frac{x}{45} + 1$.

Question 19

Write the sentence as an equation. Let the variable x represent the number.
-The product of 4 and a number increased by 5 is 32.
A) 4(x + 5) = 32
B) 4x + 5 = 32
C) 20x = 32
D) 4x - 5 = 32

Accepted Answer

The correct equation that represents the sentence is "4(x + 5) = 32," which means "the product of 4 and a number increased by 5 equals 32."

Question 20

Determine if the given value is a solution to the equation.
-x + 10 = 11; 1
A) not a solution
B) solution

Accepted Answer

Substituting x = 1 into the equation gives 1 + 10 = 11, which is true, so 1 is a solution to the equation.

Quiz 1: Variables, Real Numbers, and Mathematical Models

Write the sentence as an equation. Let the variable x represent the number. -The sum of twice a number and 5 is 11.

Write the sentence as an equation. Let the variable x represent the number. -Four times a number is 24.

Write the English phrase as an algebraic expression. Let the variable x represent the number. -the sum of 40 divided by a number and that number divided by 40

Write the sentence as an equation. Let the variable x represent the number. -Four times a number is equal to 25 decreased by the number.

Write the sentence as an equation. Let the variable x represent the number. -The product of 6 and a number, increased by 2, is 32.

Write the sentence as an equation. Let the variable x represent the number. -The quotient of 15 and a number is $\frac { 1 } { 4 }$ .

Determine if the given value is a solution to the equation. -3a + 2 = 2a + 5; 3

Write the sentence as an equation. Let the variable x represent the number. -Seven less than 4 times a number gives 5.

Determine if the given value is a solution to the equation. -3(w + 2) = 4(w - 1) ; 9

Determine if the given value is a solution to the equation. - $\frac { r } { 4 } = 5 ; 15$

Determine if the given value is a solution to the equation. -y - 2 = 1; 3

Determine if the given value is a solution to the equation. -3z = 18; 6

Write the sentence as an equation. Let the variable x represent the number. -The difference between 50 and a number is 10.

Determine if the given value is a solution to the equation. -60 - y = 10; 60

Determine if the given value is a solution to the equation. - $4 ( p - 1 ) = 2 p ; 2$

Determine if the given value is a solution to the equation. -4m + 8 = 42; 8

Write the sentence as an equation. Let the variable x represent the number. -Find the perimeter of a rectangle if the length, L, is 8 meters and the width, W, is 7 meters. Use the formula P = 2L + 2W.

Write the English phrase as an algebraic expression. Let the variable x represent the number. -one more than the quotient of a number and 45

Write the sentence as an equation. Let the variable x represent the number. -The product of 4 and a number increased by 5 is 32.

Determine if the given value is a solution to the equation. -x + 10 = 11; 1