# Mathematics - Algebra of inequalities

Please see the attached file for the fully formatted problems.

1.) Solve the equation:

2.) Pump A can fill a tank in 8 hours, and pump B can fill the same tank in 12 hours. How long will it take to fill the tank if both pumps are used?

3.) Solve by factoring:

A.) Write the three factors

B.) What are the solutions (roots)?

4.) Use the discriminant to classify the roots of the equation:

5.) Solve the equation:

6.) Solve P=2L+2W for W

7.) Solve the equation:

8.) Solve by any method:

9.) Solve the equation: -0.75r-1.25(r+1)=0.5

10.) A student has test scores of 88, 83, 99 and 96. What score does the student need on the next test to produce an average score of 90.

11.) Solve the equation 2x-3=4(6-3x)+1

12.) Solve: H

13.) How many liters of pure water should be evaporated from 7.5 liters of a 15% acid solution so that the solution that remains is a 20% acid solution?

14.) Clearly show the steps you would use to solve: y2+10y+24=0 using the completing the square method a.b.c.d.e.y=

15.) Use the quadratic formula to solve

16.) Use the quadratic formula to solve:

17.) The number N of guests that arrive at a mall food court each hour can be approximated by where x is the number of hours after 11 am. At what times to the nearest minute are 200 guests per hour arriving at the food court?

18.) Solve the inequality: x/2-2(x-3)>1

#### Solution Preview

The solution file is attached.

1.) Solve the equation:

(3/4)x - (2/3)x = 4 + 2 = 6

(9x - 8x)/12 = 6

x = 72

2.) Pump A can fill a tank in 8 hours, and [ump B can fill the same tank in 12 hours. How long will it take to fill the tank if both pumps are used?

Time taken by both the pumps to fill the tank = 1/[1/8 + 1/12] = 1/[(3 + 2)/24] = 24/5 = 4.8 hours

3.) Solve by factoring:

A.) Write the three factors

B.) What are the solutions (roots)?

(A) Given equation = x(12x^2 + 7x - 5) = x(x + 1)(12x - 5)

(B) x(x + 1)(12x - 5) = 0

The solutions are x = {0, -1, 5/12}

4.) Use the discriminant to classify the roots of the equation:

D = b^2 - 4ac = (-20)^2 - 4 * 25 * -5 = 900, which is positive

The equation has two real roots

5.) Solve the equation:

9x^2 + 13x + 4 = ...

#### Solution Summary

The expert examines inequalities in algebra. A Complete, Neat and Step-by-step Solution is provided in the attached file.