Algebra Question and Answers

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Question 1

9x + 2y = -61 …………. (1)

X = 1 – 8y  ……………  (2)

Answer:

Substitute value of x in equation 1 , we get

9(1 – 8y) + 2y = -61

• 9 – 72y +2y = -61
• Y =  70/70 = 1

 Substitute value of y in x , we get x = 1 -  8 = -7

 Solution is (-7,1).

Question 2

Determine whether (-5,2) is a solution of 5x-9y=4

Answer:

Put (-5, 2) in 5x – 9y = 4 

We get 5*(-5) – 9*2 = -25 – 18 = -43 which is not equal to 4 thus it is NOT a solution of this problem.

Question 3

Translate to an algebraic expression.  The product of 36 percentages and some number

Answer:

Let x be any some number and 36% of this number = 36x/100 = 0.36x

Question 4

Use the distributive property to solve the following questions

5(w-2) = -10

Answer:

5(w - 2) = 10

=>  5w – 10 = 10 => 5w = 20 => w = 4

Question 5

simply

9(32 – (56 - 33))

Answer:

9(32 – (56 - 33)) = 9(32 – 23 ) = 9*9 = 81

Question 6 

 Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 84 miles per hour. Train A passes a station at 7:25 PM. If tran B passes the same station at 7:55 PM.  At what time train B catch up to train A?

Answer:

Let x be the distance travelled by the train from the station 

Since Train A start its journy ½ hr before the train B start its journey. 

Suppose after t hrs both trains will meet . Thus x  = 80 (t + 1/2)

X  = 84(t)

From both equations,  80t + 40 = 84t

•     4t = 40 => t = 10 hrs
•     Thus after 10 hrs both trains will meet.  

Question 7

Graph the following equations

Y >= -3

x>= 5

Answer:

Question 8

5x/8 + x/16 = 3/16 + x

Answer:

11x/16 – x = 3/16

-5x/16 = 3/16

x = -3/5 

Question 9

-18 <= 4x – 7

Answer:

  -18 + 7 <= 4x

  -11 <= 4x        =>  -11/4 <= x  

And

4x – 7 <= -6

4x <= -6 + 7

4x <= 1

X <= ¼ 

Thus -11/4 <= x <= ¼