SOLVE LINEAR EQUATIONS WITH ONE UNKNOWN

Problem 1 :

If

3x - 4(64 - x) = 10

then the value of x is

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

Solution :

3x - 4(64 - x) = 10

3x - 256 + 4x = 10

By combining the like terms.

3x + 4x = 10 + 256

7x = 10 + 256

7x = 266

x = 266/7

x = 38

Therefore, the value of x is 38.

Problem 2 :

If

8x - 3 = 25 + 17x, then x is

(a)  a fraction   (b) an integer

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

Solution :

Given, 8x - 3 = 25 + 17x

By combining the like terms,

8x - 17x = 25 + 3

-9x = 28

x = 28/9

Therefore, the value of x is a fraction.

Problem 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

Solution :

3x - 4 = 2x + 1 ----(1)

By combining the like terms.

3x - 2x = 4 + 1

x = 5

We have, x = 5

By applying x = 5 in equation (1), we get

3x - 4 = 2x + 1

3(5) - 4 = 2(5) + 1

15 - 4 = 10 + 1

11 = 11

So, it becomes equal.

Therefore, the value of x is 5.

Problem 4 :

8x - 7 - 3x = 6x - 2x - 3

Solution :

8x - 7 - 3x = 6x - 2x - 3

By combining the like terms.

8x - 3x - 6x – 2x = 7 - 3

-x = 4

x = -4

Therefore, the value of x is -4.

Problem 5 :

10x - 5 - 7x = 5x + 15 - 8

Solution :

10x - 5 - 7x = 5x + 15 - 8

By combining the like terms.

10x – 7x – 5x = 15 – 8 + 5

-2x = 12

x = -6

Therefore the value of x is -6.

Problem 6 :

4t - 3 - (3t + 1) = 5t - 4

Solution :

4t - 3 - (3t + 1) = 5t - 4

4t - 3 - 3t -1 = 5t - 4

By combining the like terms.

4t - 3t – 5t = -4 + 3

-4t = -1

t = 1/4

Therefore the value of t is 1/4.

Problem 7 :

5(x - 1) - 2(x + 8) = 0

Solution :

5(x - 1) - 2(x + 8) = 0

5x - 5 - 2x - 8 = 0

By combining the like terms.

5x - 2x - 5 - 8 = 0

3x - 13 = 0     

10x = 0

x = 0

Therefore, the value of x is 0.

Problem 8 :

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

Solution :

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

1 - x + 2 - [x - 3 - x + 1] = 0

1 - x + 2 - x + 3 + x - 1 = 0

By combining the like terms.

1 + 2 + 3 -1 - x - x + x = 0

5 - x = 0

5 = x

Therefore, the value of x is 5.

Problem 9 :

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

Solution :

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

By using distributive property.

 12p + 8 – 30p + 5 = 2p - 16 – 42p + 24

By combining the like terms.

 12p – 30p + 5 + 8 = 2p – 42p + 24 – 16

 -18p + 13 = -40p + 8

Add 40p on both sides.

 -18p+40p+13 = 8

Subtract 13 on both sides.

 22p = 8-13

 22p = -5

Divide by 22 on both sides.

 p = -5/22

Problem 10 :

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

Solution :

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

By using distributive property.

 15x – 21 + 18x – 22 = 32x – 28x - 111

By combining the like terms.

15x + 18x – 21 – 22 = 32x – 28x - 111

 33x – 43 = 4x – 111

Subtract 4x on both sides.

33x – 43 – 4x = – 111

Add 43 on both sides.

 29x = 43 - 111

 29x = -68

Divide by 29 on both sides.

 x = -68/29