WORKSHEET ON SOLVING LINEAR EQUATIONS WITH ONE UNKNOWN

Solve the following equations with One unknown

1)  If 3x - 4(64 - x) = 10 then the value of x is

(a)  -266   (b) 133   (c) 66.5   (d) 38

2)  If 8x - 3 = 25 + 17x, then x is

(a)  a fraction   (b) an integer

(c) a rational number   (d) cannot be solved

3)  The value of x for which the expressions 3x - 4 and 2x + 1 become equal is

(a)  -3   (b) 0   (c) 5   (d) 1

4)  8x - 7 - 3x = 6x - 2x - 3

5)  10x - 5 - 7x = 5x + 15 - 8

6)  4t - 3 - (3t + 1) = 5t - 4

7)  5(x - 1) - 2(x + 8) = 0

8)  1 - (x - 2) - [(x - 3) - (x - 1)] = 0

9)   4(3p + 2) – 5(6p - 1) = 2(p - 8) – 6(7p - 4)

10)  3(5x - 7) + 2(9x  - 11) = 4(8x - 7) – 111

Solution

Solve the following equations with unknown in Denominators

1)  (3x – 8)/2x = 1

2)  5x/(2x – 1) = 2

3)  (2x – 3)/(4x + 5) = 1/3

4)  8/x = 5/(x – 1)

5)  [5(1 – x) + 3(1 + x)]/(1 – 2x) = 8 

6)  [y – (4 – 3y)] / [2y – (3 + 4y)] = 1/5

7)  (9 – 3y)/(1 – 9y) = 8/5

8)  (3x + 2)/(2x – 3) = -3/4

9)  (5x + 1)/(2x) = -1/3

10)  (x + 1)/(2x + 7) = 3/8

11)  1/(x-1) + 2/(x+1) = 2

12)  (50/x) + 4 = 14

Solution

Problem 13 :

you wrote the function c = (50m + 1000)/m, which represents the average cost c (in dollars) of making m models using a 3-D printer. Find how many models must be printed for the average cost per model to fall to $90 by

(a) solving an equation, and

(b) using the inverse of the function.

Solution

Problem 14 :

So far this baseball season, you have 12 hits out of 60 times at-bat. Solve the equation 0.360 = (12 + x) / (60 + x)   to find the number of consecutive hits you need to raise your batting average to 0.360.

Solution

Problem 1 :

The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Solution

Problem 2 :

The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

Solution

Problem 3 :

The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out  of these numbers.

Solution

Problem 4 :

Divide 54 into two parts such that one part is 2/7 of the other.

Solution

Problem 5 :

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Solution

Problem 6 :

Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.

Solution

Problem 7 :

After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

Solution

Problem 8 :

If 1/2 is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number ?

Solution

Problem 9 :

The sum of four consecutive integers is 266. What are the integers ?

Solution

Problem 10 :

Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

Solution

Problem 1 :

If 6 = 2x + 4y, what is the value of x + 2y is 

(a)  2       (b)  3     (c) 6  (d)  8

Solution

Problem 2 :

Solve for y in the equation 

and the value of y is.

(a)  -1  (b)  7   (c)  1   (d) -1/7

Solution

Problem 3 :

Pick up the correct value x for which

(a)  x = 0   (b) x = 1   (c) x = 10   (d) None of these

Solution

Problem 4 :

The denominator of the fraction exceed the numerator by 5 and if 3 be added to both the fraction becomes 3/4. Find the fraction.

(a)  12/17       (b)  15/17      (c)  12/25     (d)  13/29

Solution

Problem 5 :

Three persons Mr. Roy, Mr Paul and Mr. Singh together have $51. Mr Paul has $4 less than Mr Roy and Mr. Singh has got $5 less than Mr.Roy. They have the money as

(a)  (20, 16, 15)   (b)  (15, 20, 16)  (c)  (25, 11, 15)

Solution

Problem 6 :

A number consists of two digits. The digits in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number the digits are reversed. The number is 

(a)  39   (b)  92  (c) 93  (d)  94

Solution

Problem 7 :

The number consists of two digits, the digit in the ten's place is twice the digit in the unit's place. If 18 be subtracted from the number the digits are reversed. Find the number

(a)  42   (b)  24  (c) 33  (d)  61

Solution

Problem 8 :

Solving 4^x⋅2^y = 128 and 3^3x+2y = 9^xy, we get the following roots.

(a)  7/4, 7/2      (b)  2, 3      (c)  1, 2      (d) 1, 3

Solution

Problem 9 :

Solving 9^x = 3^y and 5^x+y+1 = 25^xy, we get the following roots.

(a)  1, 2  (b) 0, 1  (c)  0, 3  (d)  1, 3

Solution

Problem 10 :

Solving 9x + 3y - 4z =  3, x + y - z = 0 and 2x - 5y - 4z = -20 the following roots obtained.

(a) 2, 3, 4  (b) 1, 3, 4  (c) 1, 2, 3  (d) None

Solution

Problem 11 :

One machine can seal 360 packages per hour, and an older machine can seal 140 packages per hour. How many minutes will the two machines working together take to seal a total of 700 packages?

(a) 48  (b) 72  (c) 84  (d) 90

Solution

Problem 12 :

The age of a person is 8 years more than thrice the age of the sum of his two grandsons who were twins. After 8 years his age will be 10 years more then twice the sum of the ages of his grandsons. Then the age of the person when twins born is 

(a) 86 years  (b) 73 years  (c) 68 years  (d) 63 years

Solution