Linear Equations Made Great : With Practice Worksheet For Class 5th,6th,7th[11]

1) A man earns Rs.25 per hour. How much dos he earn in x hours ?

2) The cost of 1 pen is Rs. 16 and the cost of 1 pencil is Rs. 5. What is the total cost of x pens and y pencils.

3) Lalit earns Rs. x per day and spends Rs. y per day. How much does he save in 30 days ?

4) Three times a number added to 8 gives 20. Find the number.

5) If x = 1, y = 2 and z = 3, find the value of x² + y² + 2xyz.

6) Solve: 4x + 9 = 17.

7) Solve: 3(x + 2) – 2(x – 1) = 7.

8) Solve: 2x / 5 – x / 2 = 5 / 2 .

9) The sum of three consecutive natural numbers is 51. Find the number.

10) After 16 years, Seema will be three times as old as she is now. Find her present age.

11) By how much does 1 exceed 2x – 3y – 4 ? _____________

12) What must be added to 5x³ – 2x² + 6x + 7 to make the sum x³ + 3x² – x + 1 ?

13) 2x – [ 3y – { 2x – ( y – x ) } ] = ?

14) The coefficient of x in -5xyz is ? ________

15) 1 / 3 ( x + y + z ) is a ____________ term.

16) If x / 5 = 1 , find the value of x .

17) If x = 1, y = 2 and z = 3 then ( x² + y² + z² ) = ?

18) If 1x / 3 + 5 = 8, then value of x.

19)(i) An expression having one term is called _____________.

(ii) An expression having two term is called _____________.

(iii) An expression having three term is called ____________.

(iv) 3x – 5 = 7 – x, then value of x.

(v) ( b² – a² ) – ( a² – b² ) = ___________

20) Writ T” for true and ‘F’ for false.

(i) – 3xy²z is a monomial

(ii) x = 2 / 3 is a solution of 2x + 5 = 8

(iii) 2x + 3 = 5 is a linear equation

(iv) The coefficient of x in 5xy is 5

(v) 8 – x = 5, x = 3
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SOLUTIONS :
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1) Earning per hour = Rs. 25
Earning x hour = ?
Rs. ( 25x )

2) Cost of 1 pen = Rs. 16
Cost of x pens = ?
Rs. ( 16x )

Cost of 1 pencil = Rs. 5
Cost of y pencils = ?
Rs. 5y

Total cost ( 16x + 5y )

3) Earning per day = Rs. x
Spends per day = Rs. y

Savings per day = ( x – y )
Savings in 30 days = Rs. 30( x – y )

4) Let the number be x.
According to the problem,

3x + 8 = 20
3x = 20 – 8
3x = 12
x = 12 / 3
x = 4

5) x = 1 y = 2 z = 3
x² + y² + 2xyz
(1)² + (2)² + 2(1)(2)(3)
1 + 4 + 12
17

6) 4x + 9 = 17
4x = 17 – 9
4x = 8
x = 8 / 4
x = 2

7) 3 ( x + 2) – 2 ( x – 1 ) = 7
3x + 6 – 2x + 2 = 7
3x – 2x + 6 + 2 = 7
x + 8 = 7
x = 7 – 8
x = -1

8) 2x / 5 – x / 2 = 5 / 2
L.C.M = 10
4x / 10 – 5x / 10 = 25 / 10
4x – 5x = 25
-1x = 25
x = 25 / -1
x = -25

9) Let the three consecutive natural numbers = x, ( x + 1 ), ( x + 2 )
According to the problem,

x + x + 1 + x + 2 = 51
3x + 3 = 51
3x = 51 -3
3x = 48
x = 48 / 3
x = 16

x = 16
( x + 1 ) = x + 1 = 16 + 1 = 17
( x + 2 ) = x + 2 = 16 + 2 + 18

10) Let Seema’s present age be x years
After 16 years, Seema’s age = ( x + 16 ) years
According to the problem,

( x + 16 ) = 3x
x + 16 = 3x
16 = 3x – 1x
16 = 2x
16 / 2 = x
8 = x

11) 1 – ( 2x – 3y – 4 )
1 – 2x + 3y + 4
1 + 4 – 2x + 3y
5 – 2x + 3y

12) ( x³ + 3x² – x + 1 ) – ( 5x³ – 2x² + 6x + 7 )
x³ + 3x² – x + 1 – 5x³ + 2x² – 6x – 7
x³ – 5x³ + 3x²+ 2x² – x – 6x + 1 – 7
– 4x³ + 5x² – 7x – 6

13) 2x – [ 3y – { 2x – ( y – x ) } ]
2x – [ 3y – 2x – y + x ) ]
2x – ( 3y – 2x + y – x )
2x – 3y + 2x – y + x
5x – 4y

14) – 5yz

15) 1 / 3 ( x + y + z )
1x / 3 + 1y / 3 + 1z / 3
Trinomial

16) x / 5 = 1
x = 5

17) ( x² + y² + z² )
1² + 2² + 3²
1 + 4 + 9
14

18) 1x / 3 + 5 = 8
1x / 3 = 8 – 5
1x / 3 = 3
x = 3 * 3
x = 9

19) (i) Monomial

(ii) Binomial

(iii) Trinomial

(iv) 3x – 5 = 7 – x
3x + x = 7 + 5
4x = 12
x = 12 / 4
x = 3

(v) ( b² – a² ) – ( a² – b² )
b² – a² – a² + b²
b² + b² – a² – a²
2b² – 2a²
2 ( b² – a² )
2 ( b – a ) ( b + a )

20) (i) True, since it’s one term.

(ii) 2x + 5 = 8
2x = 8 – 5
2x = 3
x = 3 / 2
False

(iii) True, since, the highest power of the variable is 1

(iv) Coefficient of x in 5xy = 5y
False

(v) 8 – x = 5
8 – 5 = x
3 = x
True
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