Question 1

Solve the inequality.
-$- 8 x - 4 \leq - 2 ( 3 x + 11 )$

Accepted Answer

The answer of Solve the inequality.
-\(- 8 x - 4...

Question 2

Solve the inequality.
-$- 10 x + 1 \leq - 11 x - 6$

Accepted Answer

The answer of Solve the inequality.
-\(- 10 x + 1...

Question 3

Solve.
-The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $14 per pound. The manager wishes to mix 60 pounds of the cashews to get a cashew-peanut mixture that
Will sell for $9 per pound. How many pounds of peanuts should be used?

Accepted Answer

To find the number of pounds of peanuts needed, set up the equation based on the total cost of the mixture. Let x be the pounds of peanuts. The equation is:  6x + 14(60) = 9(x + 60).  Solving for x gives:  6x + 840 = 9x + 540,  300 = 3x,  x = 100.  So, 100 pounds of peanuts are needed.

Question 4

Solve.
-The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound.
They have a 40-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of
Raisins so that they hit their target value of $6 per pound for the mixture?

Accepted Answer

Let x be the number of pounds of nuts. The cost of the raisins is $3 per pound, so the cost of all the raisins in the barrel is 40*3 = $120. The cost of the nuts is $8 per pound, so the cost of x pounds of nuts is 8x.
The total cost of the mixture is the sum of the cost of the raisins and the cost of the nuts, which is 120 + 8x. The total weight of the mixture is 40 + x pounds. 
According to the problem, the target value of the mixture is $6 per pound. Therefore, we have the equation:
(120 + 8x)/(40 + x) = 6
Simplifying this equation, we get:
120 + 8x = 6(40 + x)
120 + 8x = 240 + 6x
2x = 120
x = 60
Therefore, they should mix 60 pounds of nuts with the 40-pound barrel of raisins. The total weight of the mixture will be 40 + 60 = 100 pounds, and the cost of the mixture will be (120 + 8*60)/100 = $6 per pound. 
Therefore, the best choice is D.

Question 5

Solve the inequality.
-$x - 6 < - 5$

Accepted Answer

The answer of Solve the inequality.
-\(x - 6 < -...

Question 6

Solve the inequality.
-$\frac { x } { 5 } \geq 6$

Accepted Answer

The answer of Solve the inequality.
-\(\frac { x } {...

Question 7

Solve the inequality.
-$12 x + 24 \leq 3 ( 3 x + 5 )$

Accepted Answer

The answer of Solve the inequality.
-\(12 x + 24 \leq...

Question 8

Solve the inequality.
-$\frac { x } { 7 } > 3$

Accepted Answer

The answer of Solve the inequality.
-\(\frac { x } {...

Question 9

Solve the inequality.
-$6 x > 114$

Accepted Answer

The answer of Solve the inequality.
-$6 x > 114$

...

Question 10

Solve the inequality.
-$- 5 \geq \frac { y } { 6 }$

Accepted Answer

The answer of Solve the inequality.
-\(- 5 \geq \frac {...

Question 11

Solve.
-A chemist needs 7 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

Accepted Answer

To find the correct amounts, set up the equation: 0.2x + 0.7(7-x) = 0.5(7). Solving gives x = 2.8 liters of the 20% solution and 4.2 liters of the 70% solution.

Question 12

Solve the inequality.
-$- 6 < \frac { y } { 2 }$

Accepted Answer

The answer of Solve the inequality.
-\(- 6 < \frac {...

Question 13

Solve the inequality.
-$10 x - 5 > 9 x - 11$

Accepted Answer

The answer of Solve the inequality.
-\(10 x - 5 >...

Question 14

Solve.
-The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $12 per pound. The manager wishes to mix 100 pounds of the $12 coffee to get a mixture that will sell for $10
Per pound. How many pounds of the $6 coffee should be used?

Accepted Answer

Let x be the number of pounds of $6 coffee needed.
We can set up the equation:
12(100) + 6x = 10(100 + x)
Solving for x, we get x = 50.
Therefore, 50 pounds of the $6 coffee should be used.

Question 15

Solve the inequality.
-$7 x \leq 91$

Accepted Answer

The answer of Solve the inequality.
-$7 x \leq 91$

...

Question 16

Solve.
-How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

To achieve an 80% acid solution, we need to find the amount of pure acid (100%) to mix with a 6-gallon 50% acid solution. Let x be the gallons of pure acid needed. The equation to represent the mixture is: 100%x + 50%(6) = 80%(x + 6). Solving for x gives x = 9 gallons.

Question 17

Solve the inequality.
-$x + 4 < - 8$

Accepted Answer

The answer of Solve the inequality.
-\(x + 4 < -...

Question 18

Solve the inequality.
-$- 4 ( 2 y - 8 ) < - 12 y + 36$

Accepted Answer

The answer of Solve the inequality.
-\(- 4 ( 2 y...

Question 19

Solve the inequality.
-$11 + 12 x - 7 \geq 11 x + 7$

Accepted Answer

The answer of Solve the inequality.
-\(11 + 12 x -...

Question 20

Solve the inequality.
-$20 x + 45 > 5 ( 3 x + 18 )$

Accepted Answer

The answer of Solve the inequality.
-\(20 x + 45 >...

Quiz 9: Equations, Inequalities, and Problem Solving

Solve the inequality. - $- 8 x - 4 \leq - 2 ( 3 x + 11 )$ $Solve the inequality. - - 8 x - 4 \leq - 2 ( 3 x + 11 ) A) \{ x \mid x \geq 9 \} B) \{ x \mid x > 9 \} C) \{ x \mid x < 9 \} D) \{ x \mid x \leq 9 \}$

Solve the inequality. - $- 10 x + 1 \leq - 11 x - 6$ $Solve the inequality. - - 10 x + 1 \leq - 11 x - 6 A) \{ x \mid x \geq - 7 \} B) \{ x \mid x > - 10 \} C) \{ x \mid x < - 10 \} D) \{ x \mid x \leq - 7 \}$

Solve. -The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $14 per pound. The manager wishes to mix 60 pounds of the cashews to get a cashew-peanut mixture that Will sell for $9 per pound. How many pounds of peanuts should be used?

Solve the inequality. - $x - 6 < - 5$ $Solve the inequality. - x - 6 < - 5 A) \{ x \mid x \geq 1 \} B) \{ x \mid x < 1 \} C) \{ x \mid x > 1 \} D) \{ x \mid x \leq 1 \}$

Solve the inequality. - $\frac { x } { 5 } \geq 6$ $Solve the inequality. - \frac { x } { 5 } \geq 6 A) \{ x \mid x \leq 30 \} B) \{ x \mid x > 30 \} C) \{ x \mid x \geq 30 \} D) \{ x \mid x < 30 \}$

Solve the inequality. - $12 x + 24 \leq 3 ( 3 x + 5 )$ $Solve the inequality. - 12 x + 24 \leq 3 ( 3 x + 5 ) A) \{ x \mid x \geq - 3 \} B) \{ x \mid x \leq - 3 \} C) \{ x \mid x > - 3 \} D) \begin{array} { l } \{ x \mid x < - 3 \} \\ \end{array}$

Solve the inequality. - $\frac { x } { 7 } > 3$ $Solve the inequality. - \frac { x } { 7 } > 3 A) \{ x \mid x < 21 \} B) \{ x \mid x \geq 21 \} C) \{ x \mid x > 21 \} D) \{ x \mid x \leq 21 \}$

Solve the inequality. - $6 x > 114$ $Solve the inequality. - 6 x > 114 A) \{ x \mid x > 19 \} B) \{ x \mid x \leq 19 \} C) \{ x \mid x \geq 19 \} D) \{ x \mid x < 19 \}$

Solve the inequality. - $- 5 \geq \frac { y } { 6 }$ $Solve the inequality. - - 5 \geq \frac { y } { 6 } A) \{ \mathrm { y } \mid \mathrm { y } > - 30 \} B) \{ \mathrm { y } \mid \mathrm { y } \leq - 30 \} C) \{ \mathrm { y } \mid \mathrm { y } < - 30 \} D) \{ y \mid y \geq - 30 \}$

Solve. -A chemist needs 7 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

Solve the inequality. - $- 6 < \frac { y } { 2 }$ $Solve the inequality. - - 6 < \frac { y } { 2 } A) \{ y \mid y > - 12 \} B) \{ \mathrm { y } \mid \mathrm { y } \leq - 12 \} C) \{ \mathrm { y } \mid \mathrm { y } < - 12 \} D) \{ \mathrm { y } \mid \mathrm { y } \geq - 12 \}$

Solve the inequality. - $10 x - 5 > 9 x - 11$ $Solve the inequality. - 10 x - 5 > 9 x - 11 A) \{ x \mid x \leq - 16 \} B) \{ x \mid x \geq - 16 \} C) \{x \mid x<-6\} D) \{ x \mid x > - 6 \}$

Solve. -The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $12 per pound. The manager wishes to mix 100 pounds of the $12 coffee to get a mixture that will sell for $10 Per pound. How many pounds of the $6 coffee should be used?

Solve the inequality. - $7 x \leq 91$ $Solve the inequality. - 7 x \leq 91 A) \{ x \mid x < 13 \} \{x \mid x<13\} B) \{ x \mid x \leq 13 \} C) \{ x \mid x \geq 13 \} D) \{ x \mid x > 13 \}$

Solve. -How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution?

Solve the inequality. - $x + 4 < - 8$ $Solve the inequality. - x + 4 < - 8 A) \{ x \mid x \geq - 12 \} B) \{x \mid x \leq-12\} C) \{x \mid x<-12\} D) \{ x \mid x > - 12 \}$

Solve the inequality. - $- 4 ( 2 y - 8 ) < - 12 y + 36$ $Solve the inequality. - - 4 ( 2 y - 8 ) < - 12 y + 36 A) \{ y \mid y > 1 \} B) \{ y \mid y \leq 1 \} C) \{ \mathrm { y } \mid \mathrm { y } < 1 \} D) \{ y \mid y \geq 1 \}$

Solve the inequality. - $11 + 12 x - 7 \geq 11 x + 7$ $Solve the inequality. - 11 + 12 x - 7 \geq 11 x + 7 A) \{ x \mid x \leq 3 \} B) \{ x \mid x > 12 \} C) \{ x \mid x \geq 3 \} D) \{x \mid x<12\}$

Solve the inequality. - $20 x + 45 > 5 ( 3 x + 18 )$ $Solve the inequality. - 20 x + 45 > 5 ( 3 x + 18 ) A) \{ x \mid x < 9 \} B) \{ x \mid x \geq 9 \} C) \{ x \mid x \leq 9 \} D) \{ x \mid x > 9 \}$

Quiz 9: Equations, Inequalities, and Problem Solving

Solve the inequality. - −8x−4≤−2(3x+11) - 8 x - 4 \leq - 2 ( 3 x + 11 ) −8x−4≤−2(3x+11)

Solve the inequality. - −10x+1≤−11x−6- 10 x + 1 \leq - 11 x - 6−10x+1≤−11x−6

Solve. -The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $14 per pound. The manager wishes to mix 60 pounds of the cashews to get a cashew-peanut mixture that Will sell for $9 per pound. How many pounds of peanuts should be used?

Solve the inequality. - x−6<−5x - 6 < - 5x−6<−5

Solve the inequality. - x5≥6\frac { x } { 5 } \geq 65x​≥6

Solve the inequality. - 12x+24≤3(3x+5) 12 x + 24 \leq 3 ( 3 x + 5 ) 12x+24≤3(3x+5)

Solve the inequality. - x7>3\frac { x } { 7 } > 37x​>3

Solve the inequality. - 6x>1146 x > 1146x>114

Solve the inequality. - −5≥y6- 5 \geq \frac { y } { 6 }−5≥6y​