Question 1

Solve the equation. $\frac { x + 3 } { 3 } + 7 = \frac { x - 3 } { 3 }$

Accepted Answer

A)  $\{ 10.5 \}$ 
B)  $\{ - 9.5 \}$ 
C)  $\{ - 10.5 \}$ 
D)  $\{ 11.5 \}$ 
E)  $\varnothing$ 
A)  $\{ 10.5 \}$ 
B)  $\{ - 9.5 \}$ 
C)  $\{ - 10.5 \}$ 
D)  $\{ 11.5 \}$ 
E)  $\varnothing$

Question 2

Perform the indicated division of polynomial by monomial. $\frac { - 36 x ^ { 13 } - 52 x ^ { 6 } } { - 4 x ^ { 2 } }$

Accepted Answer

The answer of Perform the indicated division of polynomial by...

Question 3

Solve each of the inequalities and express the solution sets in interval notation. Match each of the inequalities with the interval to obtain a true statement.
-$( - \infty , 30 ]$

Accepted Answer

A)  $0.01 x + 0.09 ( 400 - x ) \geq 33.6$ 
B)  $0.06 x + 0.9 ( x + 100 ) > 858$ 
C)  $x \geq 3.18 + 0.47 x$ 
A)  $0.01 x + 0.09 ( 400 - x ) \geq 33.6$ 
B)  $0.06 x + 0.9 ( x + 100 ) > 858$ 
C)  $x \geq 3.18 + 0.47 x$

Question 4

Find the indicated product. ( x 2 + 9 x + 9)( x 2 + 9 x + 2)

Accepted Answer

A)  x 4 + 18 x 3 + 11 x 2 + 99 x + 18 
B)  x 4 + 18 x 3 + 92 x 2 + 18 x + 18 
C)  x 4 + 18 x 3 + 92 x 2 + 99 x + 2 
D)  x 4 + 18 x 3 + 92 x 2 + 99 x + 18 
A)  x 4 + 18 x 3 + 11 x 2 + 99 x + 18 
B)  x 4 + 18 x 3 + 92 x 2 + 18 x + 18 
C)  x 4 + 18 x 3 + 92 x 2 + 99 x + 2 
D)  x 4 + 18 x 3 + 92 x 2 + 99 x + 18

Question 5

Solve the inequality and express the solution sets in interval notation. $0.02 x + 0.06 ( 2 x ) \geq 112$

Accepted Answer

The answer of Solve the inequality and express the solution...

Question 6

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

Accepted Answer

A)  Q: $4 x ^ { 2 } - 2 x + 7$
R: 0 
B)  Q: $4 x ^ { 2 } - 2 x + 7$
R: $\frac { 9 } { 2 }$ 
C)  $\begin{array} { l } 
\mathrm { Q } : 4 x ^ { 2 } + 2 x - 7 \
\mathrm { R } : - \frac { 9 } { 2 }
\end{array}$ 
D)  $\begin{array} { l } 
\mathrm { Q } : 4 x ^ { 2 } - 2 x + 7 \
\mathrm { R } : - \frac { 9 } { 2 }
\end{array}$ 
E)  Q: $4 x ^ { 2 } + 2 x - 7$
$\mathrm { R } : \frac { 9 } { 2 }$ 
A)  Q: $4 x ^ { 2 } - 2 x + 7$
R: 0 
B)  Q: $4 x ^ { 2 } - 2 x + 7$
R: $\frac { 9 } { 2 }$ 
C)  $\begin{array} { l } 
\mathrm { Q } : 4 x ^ { 2 } + 2 x - 7 \
\mathrm { R } : - \frac { 9 } { 2 }
\end{array}$ 
D)  $\begin{array} { l } 
\mathrm { Q } : 4 x ^ { 2 } - 2 x + 7 \
\mathrm { R } : - \frac { 9 } { 2 }
\end{array}$ 
E)  Q: $4 x ^ { 2 } + 2 x - 7$
$\mathrm { R } : \frac { 9 } { 2 }$

Question 7

Find the indicated product. Assume all variables that appear as exponents represent positive integers. ( x 5 a $-$ 4)( x 5 a + 4)

Accepted Answer

A)  x 10 a $-$ 16 
B)  x 10 a $-$ 4 
C)  x 5 a $-$ 16 
D)  x 10 a  + 16 
A)  x 10 a $-$ 16 
B)  x 10 a $-$ 4 
C)  x 5 a $-$ 16 
D)  x 10 a  + 16

Question 8

Solve the equation. | 6 x $-$ 42 | + 6 = 24

Accepted Answer

A)  x = 4 
B)  x = $-$ 4, x = $-$ 10 
C)  x = 10 
D)  x = 4, x = 10 
A)  x = 4 
B)  x = $-$ 4, x = $-$ 10 
C)  x = 10 
D)  x = 4, x = 10

Question 9

Solve the equation. $9 ( 2 x + 3 ) = 7 ( 3 x - 2 )$

Accepted Answer

A)  $\left\{ - \frac { 38 } { 3 } \right\}$ 
B)  $\left\{ \frac { 38 } { 3 } \right\}$ 
C)  $\left\{ \frac { 41 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 41 } { 3 } \right\}$ 
E)  $\varnothing$ 
A)  $\left\{ - \frac { 38 } { 3 } \right\}$ 
B)  $\left\{ \frac { 38 } { 3 } \right\}$ 
C)  $\left\{ \frac { 41 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 41 } { 3 } \right\}$ 
E)  $\varnothing$

Question 10

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 1 \right) \left( 3 x ^ { n } - 1 \right)$

Accepted Answer

A)  $6 x ^ { n } { } ^ { 2 } - x ^ { n } + 1$ 
B)  $6 x ^ { 2 n } - x ^ { n } - 1$ 
C)  $6 x ^ { 2 n } + x ^ { n } - 1$ 
D)  $6 x ^ { n } { } ^ { 2 } + x ^ { n } - 1$ 
E)  $6 x ^ { 2 n } - x ^ { n } + 1$ 
A)  $6 x ^ { n } { } ^ { 2 } - x ^ { n } + 1$ 
B)  $6 x ^ { 2 n } - x ^ { n } - 1$ 
C)  $6 x ^ { 2 n } + x ^ { n } - 1$ 
D)  $6 x ^ { n } { } ^ { 2 } + x ^ { n } - 1$ 
E)  $6 x ^ { 2 n } - x ^ { n } + 1$

Question 11

The Ortegas have an apple orchard that contains 70 trees. The number of trees in each row is 4 more than twice the number of rows. Find the number of rows and the number of trees per row.

Accepted Answer

A)  5 rows with 9 trees per row 
B)  9 rows with 14 trees per row 
C)  5 rows with 14 trees per row 
A)  5 rows with 9 trees per row 
B)  9 rows with 14 trees per row 
C)  5 rows with 14 trees per row

Question 12

Factor the polynomial completely. $1 - 36 n ^ { 2 }$

Accepted Answer

A)  $( 1 + 6 n ) ( 1 - 6 n )$ 
B)  $( 1 + 36 n ) ( 1 - n )$ 
C)  $( 6 + 1 n ) ( 1 - 6 n )$ 
D)  $( 1 + n ) ( 1 - 36 n )$ 
E)  not factorable 
A)  $( 1 + 6 n ) ( 1 - 6 n )$ 
B)  $( 1 + 36 n ) ( 1 - n )$ 
C)  $( 6 + 1 n ) ( 1 - 6 n )$ 
D)  $( 1 + n ) ( 1 - 36 n )$ 
E)  not factorable

Question 13

The perimeter of a rectangle is 14 inches and the area is 12 square inches. Find the length and width of the rectangle.

Accepted Answer

A)  6 inches and 8 inches 
B)  6 inches and 4 inches 
C)  3 inches and 4 inches 
A)  6 inches and 8 inches 
B)  6 inches and 4 inches 
C)  3 inches and 4 inches

Question 14

Solve the equation by inspection. | 2 x $-$ 4 | = 0

Accepted Answer

The answer of Solve the equation by inspection. | 2...

Question 15

The notation $( - \infty , 3 ]$ refers to the interval of all real numbers greater than 3.

Accepted Answer

A) True 
 B)False

Question 16

Solve the equation. $\frac { 2 } { 3 } x - \frac { 1 } { 2 } + \frac { 1 } { 4 } x = \frac { 9 } { 8 }$

Accepted Answer

The answer of Solve the equation. \(\frac { 2 }...

Question 17

Solve each compound inequality. Express the solution sets in interval notation. Match each compound inequality with the interval to obtain a true statement.
-$\left( \frac { 1 } { 13 } , \frac { 14 } { 15 } \right)$

Accepted Answer

A)  $15 x - 14  0$ 
B)  $x + 1 > 0 \text { and } 13 x - 14  13$ 
D)  $15 x - 14  8$ 
A)  $15 x - 14  0$ 
B)  $x + 1 > 0 \text { and } 13 x - 14  13$ 
D)  $15 x - 14  8$

Question 18

When an equation contains fractional forms, multiply both sides by the greatest common factor of all of the denominators.

Accepted Answer

A) True 
 B)False

Question 19

Solve the inequality and express the solution set using interval notation. $- ( x - 2 ) + 4 ( x - 4 ) < 22 ( x + 3 )$

Accepted Answer

A)  $\left[ - \frac { 80 } { 19 } , + \infty \right)$ 
B)  $\left( - \infty , - \frac { 80 } { 19 } \right]$ 
C)  $\left( - \infty , - \frac { 80 } { 19 } \right)$ 
D)  $\left( - \frac { 80 } { 19 } , + \infty \right)$ 
A)  $\left[ - \frac { 80 } { 19 } , + \infty \right)$ 
B)  $\left( - \infty , - \frac { 80 } { 19 } \right]$ 
C)  $\left( - \infty , - \frac { 80 } { 19 } \right)$ 
D)  $\left( - \frac { 80 } { 19 } , + \infty \right)$

Question 20

Solve the equation using factoring techniques. 2 n 3 = 8 n Please enter your answer as three numbers, separated by commas.

Accepted Answer

Solve the equation. $\frac { x + 3 } { 3 } + 7 = \frac { x - 3 } { 3 }$

Perform the indicated division of polynomial by monomial. $\frac { - 36 x ^ { 13 } - 52 x ^ { 6 } } { - 4 x ^ { 2 } }$

Solve each of the inequalities and express the solution sets in interval notation. Match each of the inequalities with the interval to obtain a true statement. - $( - \infty , 30 ]$

Find the indicated product. ( x ² + 9 x + 9)( x ² + 9 x + 2)

Solve the inequality and express the solution sets in interval notation. $0.02 x + 0.06 ( 2 x ) \geq 112$

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

Find the indicated product. Assume all variables that appear as exponents represent positive integers. ( x 5 a $-$ 4)( x 5 a + 4)

Solve the equation. | 6 x $-$ 42 | + 6 = 24

Solve the equation. $9 ( 2 x + 3 ) = 7 ( 3 x - 2 )$

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 1 \right) \left( 3 x ^ { n } - 1 \right)$

The Ortegas have an apple orchard that contains 70 trees. The number of trees in each row is 4 more than twice the number of rows. Find the number of rows and the number of trees per row.

Factor the polynomial completely. $1 - 36 n ^ { 2 }$

The perimeter of a rectangle is 14 inches and the area is 12 square inches. Find the length and width of the rectangle.

Solve the equation by inspection. | 2 x $-$ 4 | = 0

The notation $( - \infty , 3 ]$ refers to the interval of all real numbers greater than 3.

Solve the equation. $\frac { 2 } { 3 } x - \frac { 1 } { 2 } + \frac { 1 } { 4 } x = \frac { 9 } { 8 }$

Solve each compound inequality. Express the solution sets in interval notation. Match each compound inequality with the interval to obtain a true statement. - $\left( \frac { 1 } { 13 } , \frac { 14 } { 15 } \right)$

When an equation contains fractional forms, multiply both sides by the greatest common factor of all of the denominators.

Solve the inequality and express the solution set using interval notation. $- ( x - 2 ) + 4 ( x - 4 ) < 22 ( x + 3 )$

Solve the equation using factoring techniques. 2 n ³ = 8 n Please enter your answer as three numbers, separated by commas.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 8: A Transition From Elementary Algebra to Intermediate Algebra

Solve the equation. x+33+7=x−33\frac { x + 3 } { 3 } + 7 = \frac { x - 3 } { 3 }3x+3​+7=3x−3​

Perform the indicated division of polynomial by monomial. −36x13−52x6−4x2\frac { - 36 x ^ { 13 } - 52 x ^ { 6 } } { - 4 x ^ { 2 } }−4x2−36x13−52x6​

Solve each of the inequalities and express the solution sets in interval notation. Match each of the inequalities with the interval to obtain a true statement. - (−∞,30]( - \infty , 30 ](−∞,30]

Find the indicated product. ( x 2 + 9 x + 9)( x 2 + 9 x + 2)

Solve the inequality and express the solution sets in interval notation. 0.02x+0.06(2x)≥1120.02 x + 0.06 ( 2 x ) \geq 1120.02x+0.06(2x)≥112

Use synthetic division to determine the quotient and remainder for the division problem. (4x3+4x2−6x+1)÷(x+12)\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)(4x3+4x2−6x+1)÷(x+21​)

Find the indicated product. Assume all variables that appear as exponents represent positive integers. ( x 5 a −-− 4)( x 5 a + 4)

Solve the equation. | 6 x −-− 42 | + 6 = 24

Solve the equation. 9(2x+3)=7(3x−2)9 ( 2 x + 3 ) = 7 ( 3 x - 2 )9(2x+3)=7(3x−2)

Find the indicated product. Assume the variable that appears as exponent represents positive integer. (2xn+1)(3xn−1)\left( 2 x ^ { n } + 1 \right) \left( 3 x ^ { n } - 1 \right)(2xn+1)(3xn−1)

The Ortegas have an apple orchard that contains 70 trees. The number of trees in each row is 4 more than twice the number of rows. Find the number of rows and the number of trees per row.

Factor the polynomial completely. 1−36n21 - 36 n ^ { 2 }1−36n2

The perimeter of a rectangle is 14 inches and the area is 12 square inches. Find the length and width of the rectangle.

Solve the equation by inspection. | 2 x −-− 4 | = 0

The notation (−∞,3]( - \infty , 3 ](−∞,3] refers to the interval of all real numbers greater than 3.

Solve the equation. 23x−12+14x=98\frac { 2 } { 3 } x - \frac { 1 } { 2 } + \frac { 1 } { 4 } x = \frac { 9 } { 8 }32​x−21​+41​x=89​

Solve each compound inequality. Express the solution sets in interval notation. Match each compound inequality with the interval to obtain a true statement. - (113,1415)\left( \frac { 1 } { 13 } , \frac { 14 } { 15 } \right)(131​,1514​)

When an equation contains fractional forms, multiply both sides by the greatest common factor of all of the denominators.

Solve the inequality and express the solution set using interval notation. −(x−2)+4(x−4)<22(x+3)- ( x - 2 ) + 4 ( x - 4 ) < 22 ( x + 3 )−(x−2)+4(x−4)<22(x+3)

Solve the equation using factoring techniques. 2 n 3 = 8 n Please enter your answer as three numbers, separated by commas.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Solve the equation. $\frac { x + 3 } { 3 } + 7 = \frac { x - 3 } { 3 }$

Perform the indicated division of polynomial by monomial. $\frac { - 36 x ^ { 13 } - 52 x ^ { 6 } } { - 4 x ^ { 2 } }$

Solve each of the inequalities and express the solution sets in interval notation. Match each of the inequalities with the interval to obtain a true statement. - $( - \infty , 30 ]$

Find the indicated product. ( x ² + 9 x + 9)( x ² + 9 x + 2)

Solve the inequality and express the solution sets in interval notation. $0.02 x + 0.06 ( 2 x ) \geq 112$

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

Find the indicated product. Assume all variables that appear as exponents represent positive integers. ( x 5 a $-$ 4)( x 5 a + 4)

Solve the equation. | 6 x $-$ 42 | + 6 = 24

Solve the equation. $9 ( 2 x + 3 ) = 7 ( 3 x - 2 )$

Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 2 x ^ { n } + 1 \right) \left( 3 x ^ { n } - 1 \right)$

Factor the polynomial completely. $1 - 36 n ^ { 2 }$

Solve the equation by inspection. | 2 x $-$ 4 | = 0

The notation $( - \infty , 3 ]$ refers to the interval of all real numbers greater than 3.

Solve the equation. $\frac { 2 } { 3 } x - \frac { 1 } { 2 } + \frac { 1 } { 4 } x = \frac { 9 } { 8 }$

Solve each compound inequality. Express the solution sets in interval notation. Match each compound inequality with the interval to obtain a true statement. - $\left( \frac { 1 } { 13 } , \frac { 14 } { 15 } \right)$

Solve the inequality and express the solution set using interval notation. $- ( x - 2 ) + 4 ( x - 4 ) < 22 ( x + 3 )$

Solve the equation using factoring techniques. 2 n ³ = 8 n Please enter your answer as three numbers, separated by commas.