Question 1

Solve the equation.
- 65x−1x+1=3x(2x+2) \frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 )  }5x6​−x+11​=x(2x+2) 3​

Accepted Answer

A)    {3}\{ 3 \}{3} 
B)    {310}\left\{ \frac { 3 } { 10 } \right\}{103​} 
C)    {32}\left\{ \frac { 3 } { 2 } \right\}{23​} 
D)   no solution E) C) and D)
F) None of the above

Question 2

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
- 11−3(3−x) ≤1411 - 3 ( 3 - x )  \leq 1411−3(3−x) ≤14

Accepted Answer

A)    (−∞,5]( - \infty , 5 ](−∞,5] 
B)    (−∞,4) ( - \infty , 4 ) (−∞,4)  
C)   [4,∞) [ 4 , \infty ) [4,∞)  
D)    (−∞,4]( - \infty , 4 ](−∞,4]  E) B) and C)
F) A) and B)

Question 3

Solve the equation using the square root property.
- (2x−3) 2−49=0( 2 x - 3 )  ^ { 2 } - 49 = 0(2x−3) 2−49=0

Accepted Answer

A)    {10,−4}\{ 10 , - 4 \}{10,−4} 
B)    {4,−10}\{ 4 , - 10 \}{4,−10} 
C)    {5,−2}\{ 5 , - 2 \}{5,−2} 
D)    {2,−5}\{ 2 , - 5 \}{2,−5}E) A) and C)
F) B) and C)

Question 4

Solve the equation.
- ∣x2−6x∣=0\left| x ^ { 2 } - 6 x \right| = 0​x2−6x​=0

Accepted Answer

A)    {−6,0}\{ - 6,0 \}{−6,0} 
B)    {0,6}\{ 0,6 \}{0,6} 
C)    {−6,0,6}\{ - 6,0,6 \}{−6,0,6} 
D)   no real solution E) A) and D)
F) B) and C)

Question 5

Solve the problem.
-Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

Accepted Answer

A)  35 hr
B)  50 hr
C)  70 hr
D)  15 hrE) A) and B)
F) None of the above

Question 6

Solve the polynomial inequality. Express the solution in interval notation.
-  0">x3−4x2>0x ^ { 3 } - 4 x ^ { 2 } > 0x3−4x2>0

Accepted Answer

A)    (4,∞) ( 4 , \infty ) (4,∞)  
B)    (−∞,0) ∪(4,∞) ( - \infty , 0 )  \cup ( 4 , \infty ) (−∞,0) ∪(4,∞)  
C)    (0,4) ( 0,4 ) (0,4)  
D)    (−∞,4) ( - \infty , 4 ) (−∞,4) E) B) and D)
F) C) and D)

Question 7

Solve the polynomial inequality. Express the solution in interval notation.
- (x+5) (x−5) ≤0( x + 5 )  ( x - 5 )  \leq 0(x+5) (x−5) ≤0

Accepted Answer

A)    (−5,5) ( - 5,5 ) (−5,5)  
B)    (−∞,−5) ∪(5,∞) ( - \infty , - 5 )  \cup ( 5 , \infty ) (−∞,−5) ∪(5,∞)  
C)    (−∞,−5]∪[5,∞) ( - \infty , - 5 ] \cup [ 5 , \infty ) (−∞,−5]∪[5,∞)  
D)    [−5,5][ - 5,5 ][−5,5]E) C) and D)
F) A) and B)

Question 8

Solve the equation by factoring.
- x2+x−20=0x ^ { 2 } + x - 20 = 0x2+x−20=0

Accepted Answer

A)    {4,5}\{ 4,5 \}{4,5} 
B)    {−5,−4}\{ - 5 , - 4 \}{−5,−4} 
C)    {−5,4}\{ - 5,4 \}{−5,4} 
D)    {−4,5}\{ - 4,5 \}{−4,5}E) All of the above
F) None of the above

Question 9

Solve the polynomial inequality. Express the solution in interval notation.
-  0">(x−1) (x+8) >0( x - 1 )  ( x + 8 )  > 0(x−1) (x+8) >0

Accepted Answer

A)   (−8,∞ (- 8 ,  \infty (−8,∞ ) 
B)    (−8,1) ( - 8,1 ) (−8,1)  
C)    (−∞,−1) ∪(8,∞) ( - \infty , - 1 )  \cup ( 8 , \infty ) (−∞,−1) ∪(8,∞)  
D)    (−∞,−8) ∪(1,∞) ( - \infty , - 8 )  \cup ( 1 , \infty ) (−∞,−8) ∪(1,∞) E) A) and C)
F) A) and B)

Question 10

Write the power of i as i, -1, -i, or 1.
- i8\mathrm { i } 8i8

Accepted Answer

A)  1
B)  i
C)  -i
D)  -1 E) B) and D)
F) B) and C)

Question 11

Solve the equation after making an appropriate substitution.
- x+x=72x + \sqrt { x } = 72x+x​=72

Accepted Answer

A)    {8}\{ 8 \}{8} 
B)    {9}\{ 9 \}{9} 
C)    {81}\{ 81 \}{81} 
D)    {64}\{ 64 \}{64}E) B) and C)
F) A) and D)

Question 12

Solve the equation.
--4x + 1 - 4(x + 1) = -6x + 1

Accepted Answer

A)    {−74}\left\{ - \frac { 7 } { 4 } \right\}{−47​} 
B)    {35}\left\{ \frac { 3 } { 5 } \right\}{53​} 
C)    {−6}\{ - 6 \}{−6} 
D)    {−2}\{ - 2 \}{−2}E) A) and D)
F) B) and C)

Question 13

Solve the equation.
--35 - 3x = -10 + 2x

Accepted Answer

A)    {−7}\{ - 7 \}{−7} 
B)    {−5}\{ - 5 \}{−5} 
C)    {5}\{ 5 \}{5} 
D)    {7}\{ 7 \}{7}E) B) and C)
F) A) and D)

Question 14

Solve the rational inequality. Express the solution in interval notation.
-  \frac { 12 } { x + 1 }">14x−6>12x+1\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }x−614​>x+112​

Accepted Answer

A)    (−43,−1) ∪(6,∞) ( - 43 , - 1 )  \cup ( 6 , \infty ) (−43,−1) ∪(6,∞)  
B)    (−∞,−43) ∪(−1,6) ( - \infty , - 43 )  \cup ( - 1,6 ) (−∞,−43) ∪(−1,6)  
C)    (−43,−1) ∪(−1,6) ( - 43 , - 1 )  \cup ( - 1,6 ) (−43,−1) ∪(−1,6)  
D)    (−∞,−43) ∪(6,∞) ( - \infty , - 43 )  \cup ( 6 , \infty ) (−∞,−43) ∪(6,∞) E) None of the above
F) B) and C)

Question 15

Find all solutions.
- x3+2x2−9x−18=0x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0x3+2x2−9x−18=0

Accepted Answer

A)    {−3,3,2}\{ - 3,3,2 \}{−3,3,2} 
B)    {−3,3,−2}\{ - 3,3 , - 2 \}{−3,3,−2} 
C)    {9,−2}\{ 9 , - 2 \}{9,−2} 
D)    {3,−2}\{ 3 , - 2 \}{3,−2}E) A) and B)
F) A) and C)

Question 16

Perform the indicated operations and write the result in standard form.
- −4⋅−36\sqrt { - 4 } \cdot \sqrt { - 36 }−4​⋅−36​

Accepted Answer

A)    −12i- 12 \mathrm { i }−12i 
B)    −12- 12−12 
C)   12
D)    12i212 \mathrm { i } ^ { 2 }12i2E) All of the above
F) A) and D)

Question 17

Perform the indicated operations and write the result in standard form.
- −49+−81\sqrt { - 49 } + \sqrt { - 81 }−49​+−81​

Accepted Answer

A)    −16- 16−16 
B)    16i16 \mathrm { i }16i 
C)    −16i- 16 \mathrm { i }−16i 
D)    63i63 \mathrm { i }63iE) None of the above
F) B) and D)

Question 18

Solve the equation.
- 25x=3+13x\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x52​x=3+31​x

Accepted Answer

A)    {−45}\{ - 45 \}{−45} 
B)    {45}\{ 45 \}{45} 
C)    {90}\{ 90 \}{90} 
D)    {−90}\{ - 90 \}{−90}E) None of the above
F) A) and C)

Question 19

Solve the problem.
-A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

Accepted Answer

A)  $3100
B)  $983
C)  $2800
D)  $2950E) All of the above
F) A) and C)

Question 20

Perform the desired operation. Write the answer in the form a + bi.
- (8+2i) (6−6i) ( 8 + 2 \mathrm { i } )  ( 6 - 6 \mathrm { i } ) (8+2i) (6−6i)

Accepted Answer

A)    60−36i60 - 36 \mathrm { i }60−36i 
B)    −12i2−36i+48- 12 i ^ { 2 } - 36 i + 48−12i2−36i+48 
C)    60+36i60 + 36 i60+36i 
D)    36+60i36 + 60 \mathrm { i }36+60iE) A) and B)
F) B) and D)

Exam 1: Equations, Inequalities, and Applications

Solve the equation using the square root property. - $( 2 x - 3 ) ^ { 2 } - 49 = 0$

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $( x - 1 ) ( x + 8 ) > 0$

Correct Answer
verified

Solve the equation by factoring. - $x ^ { 2 } + x - 20 = 0$

Correct Answer
verified

Solve the equation. - $\left| x ^ { 2 } - 6 x \right| = 0$

Correct Answer
verified

Solve the problem. -Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

Correct Answer
verified

Solve the equation. --35 - 3x = -10 + 2x

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $( x + 5 ) ( x - 5 ) \leq 0$

Correct Answer
verified

Solve the equation. --4x + 1 - 4(x + 1) = -6x + 1

Correct Answer
verified

Solve the equation. - $\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }$

Correct Answer
verified

Perform the indicated operations and write the result in standard form. - $\sqrt { - 4 } \cdot \sqrt { - 36 }$

Correct Answer
verified

Correct Answer
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Perform the indicated operations and write the result in standard form. - $\sqrt { - 49 } + \sqrt { - 81 }$

Correct Answer
verified

Solve the problem. -A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

Correct Answer
verified

Perform the desired operation. Write the answer in the form a + bi. - $( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )$

Correct Answer
verified

Solve the equation after making an appropriate substitution. - $x + \sqrt { x } = 72$

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 3 } - 4 x ^ { 2 } > 0$

Correct Answer
verified

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } 8$

Correct Answer
verified

Solve the rational inequality. Express the solution in interval notation. - $\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }$

Correct Answer
verified

Find all solutions. - $x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0$

Correct Answer
verified

Solve the equation. - $\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x$

Correct Answer
verified

Exam 1: Equations, Inequalities, and Applications

Solve the equation using the square root property. - (2x−3) 2−49=0( 2 x - 3 ) ^ { 2 } - 49 = 0(2x−3) 2−49=0

Correct AnswerverifiedShow Answer

Solve the polynomial inequality. Express the solution in interval notation. - (x−1) (x+8) >0( x - 1 ) ( x + 8 ) > 0(x−1) (x+8) >0

Correct AnswerverifiedShow Answer

Solve the equation by factoring. - x2+x−20=0x ^ { 2 } + x - 20 = 0x2+x−20=0

Correct AnswerverifiedShow Answer

Solve the equation. - ∣x2−6x∣=0\left| x ^ { 2 } - 6 x \right| = 0​x2−6x​=0

Correct AnswerverifiedShow Answer

Solve the problem. -Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

Correct AnswerverifiedShow Answer

Solve the equation. --35 - 3x = -10 + 2x

Correct AnswerverifiedShow Answer

Solve the polynomial inequality. Express the solution in interval notation. - (x+5) (x−5) ≤0( x + 5 ) ( x - 5 ) \leq 0(x+5) (x−5) ≤0

Correct AnswerverifiedShow Answer

Solve the equation. --4x + 1 - 4(x + 1) = -6x + 1

Correct AnswerverifiedShow Answer

Solve the equation. - 65x−1x+1=3x(2x+2) \frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }5x6​−x+11​=x(2x+2) 3​

Correct AnswerverifiedShow Answer

Perform the indicated operations and write the result in standard form. - −4⋅−36\sqrt { - 4 } \cdot \sqrt { - 36 }−4​⋅−36​

Correct AnswerverifiedShow Answer

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - 11−3(3−x) ≤1411 - 3 ( 3 - x ) \leq 1411−3(3−x) ≤14

Correct AnswerverifiedShow Answer

Perform the indicated operations and write the result in standard form. - −49+−81\sqrt { - 49 } + \sqrt { - 81 }−49​+−81​

Correct AnswerverifiedShow Answer

Solve the problem. -A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

Correct AnswerverifiedShow Answer

Perform the desired operation. Write the answer in the form a + bi. - (8+2i) (6−6i) ( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } ) (8+2i) (6−6i)

Correct AnswerverifiedShow Answer

Solve the equation after making an appropriate substitution. - x+x=72x + \sqrt { x } = 72x+x​=72

Correct AnswerverifiedShow Answer

Solve the polynomial inequality. Express the solution in interval notation. - x3−4x2>0x ^ { 3 } - 4 x ^ { 2 } > 0x3−4x2>0

Correct AnswerverifiedShow Answer

Write the power of i as i, -1, -i, or 1. - i8\mathrm { i } 8i8

Correct AnswerverifiedShow Answer

Solve the rational inequality. Express the solution in interval notation. - 14x−6>12x+1\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }x−614​>x+112​

Correct AnswerverifiedShow Answer

Find all solutions. - x3+2x2−9x−18=0x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0x3+2x2−9x−18=0

Correct AnswerverifiedShow Answer

Solve the equation. - 25x=3+13x\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x52​x=3+31​x

Correct AnswerverifiedShow Answer

Solve the equation using the square root property. - $( 2 x - 3 ) ^ { 2 } - 49 = 0$

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $( x - 1 ) ( x + 8 ) > 0$

Correct Answer
verified

Solve the equation by factoring. - $x ^ { 2 } + x - 20 = 0$

Correct Answer
verified

Solve the equation. - $\left| x ^ { 2 } - 6 x \right| = 0$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $( x + 5 ) ( x - 5 ) \leq 0$

Correct Answer
verified

Correct Answer
verified

Solve the equation. - $\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }$

Correct Answer
verified

Perform the indicated operations and write the result in standard form. - $\sqrt { - 4 } \cdot \sqrt { - 36 }$

Correct Answer
verified

Correct Answer
verified

Perform the indicated operations and write the result in standard form. - $\sqrt { - 49 } + \sqrt { - 81 }$

Correct Answer
verified

Correct Answer
verified

Perform the desired operation. Write the answer in the form a + bi. - $( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )$

Correct Answer
verified

Solve the equation after making an appropriate substitution. - $x + \sqrt { x } = 72$

Correct Answer
verified

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 3 } - 4 x ^ { 2 } > 0$

Correct Answer
verified

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } 8$

Correct Answer
verified

Solve the rational inequality. Express the solution in interval notation. - $\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }$

Correct Answer
verified

Find all solutions. - $x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0$

Correct Answer
verified

Solve the equation. - $\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x$

Correct Answer
verified