Chapter 4: Linear Equations in One Variable

Solution:-

We have,

((2x – 3)/(4x + 5)) = (1/3)

By cross multiplication, we get

3 × (2x – 3) = 1 × (4x + 5)

6x – 9 = 4x + 5

Transposing -9 to RHS, it becomes 9 and 4x to LHS, it becomes – 4x.

6x – 4x = 5 + 9

2x = 14

x = 14/2

x = 7

Solution:-

We have,

(8/x) = (5/(x – 1))

By cross multiplication, we get

8 × (x – 1) = 5 × x

8x – 8 = 5x

Transposing -8 to RHS, it becomes 8 and 5x to LHS, it becomes – 5x.

8x – 5x = 8

3x = 8

X = 8/3

Solution:-

We have,

By cross multiplication, we get

(5(1 – x)) + (3(1 + x)) = 8 × (1 – 2x)

5 – 5x + 3 + 3x = 8 – 16 x

8 – 2x = 8 – 16x

Transposing 8 to RHS, it becomes – 8 and -16x to LHS, it becomes 16x.

16x – 2x = 8 – 8

14x = 0

x = 0/14

x = 0

Solution:-

We have,

((0.2x + 5)/ (3.5x – 3)) = (2/5)

By cross multiplication, we get

5 × (0.2x + 5) = 2 × (3.5x – 3)

x + 25 = 7x – 6

Transposing x to RHS, it becomes – x and -6 to LHS, it becomes 6.

25 + 6 = 7x – x

31 = 6x

x = 31/6

Solution:-

We have,

(y – 4 + 3y)/ (2y – 3 – 4y) = 1/5

(-4y – 4)/ (2y – 3) = 1/5

By cross multiplication, we get

5 × (-4y – 4) = 1 × (2y – 3)

20y – 20 = 2y – 3

Transposing – 20 to RHS it becomes 20 and 6y to LHS it becomes -6y.

20y – 2y = 20 – 3

22 y = 17

y = 17/22

Solution:-

We have,

(x/5) = (x – 1)/6

By cross multiplication, we get

6 × x = 5 × (x – 1)

6x = 5x – 5

Transposing 5x to RHS it becomes -5x

6x – 5x = -5

x = -5

Solution:-

We have,

0.4(3x –1) = 0.5x + 1

1.2x – 0.4 = 0.5x + 1

Transposing – 0.4 to RHS, it becomes 0.4 and 0.5x to LHS, it becomes -0.5x.

1.2x – 0.5x = 1 + 0.4

0.7x = 1.4

x = 1.4/0.7

x = 14/7

x = 2

Solution:-

We have,

8x – 7 – 3x = 6x – 2x – 3

5x – 7 = 4x – 3

Transposing – 7 to RHS it becomes 7 and 4x to LHS it becomes -4x.

5x – 4x = 7 – 3

x = 4

Solution:-

We have,

10x – 5 – 7x = 5x + 15 – 8

3x – 5 = 5x + 7

Transposing – 5 to RHS, it becomes 5 and 5x to LHS, it becomes -5x.

3x – 5x = 7 + 5

– 2x = 12

x = -12/2

x = – 6

Solution:-

We have,

4t – 3 – (3t +1) = 5t – 4

4t – 3 – 3t – 1 = 5t – 4

t – 4 = 5t – 4

Transposing t to RHS, it becomes -t and -4 to LHS it becomes 4.

4 – 4 = 5t – t

0 = 4t

t = 0/4

t = 0