Linear Equations in One Variable - 8th math

Solve the following linear equations.

Question (1)

Solution

Given,

After transposing –1/5 to RHS, we get

After transposing x/3 to LHS, we get

After cross multiplication, we get

20x = 9 × 6

⇒ 20x = 54

After transposing 20 to RHS, we get

Checking of Result

Given,

Now, LHS

Now, after substituting the value of , we get

Thus, LHS

Now, RHS =

Now, after substituting the value of in RHS, we get

Thus, RHS

Thus, LHS = RHS Proved

Thus, Answer

Question (2)

Solution:

Given

After cross multiplication, we get

⇒ 7n = 21 × 12

⇒ 7n = 252

After transposing 7 to RHS, we get

⇒ n = 36

Checking of Result

Given

Now, after substituting the value of n = 36 in LHS, we get

= 18 – 27 + 30

= 21 = RHS

Thus, LHS = RHS Proved

Thus, n = 36 Answer

Question (3)

Solution

Given,

After transposing to LHS, we get

Again after transposing 7 to RHS, we get

After multiplying both sides by 6 we get

⇒ 5x = –25

After transposing 5 to RHS, we get

⇒ x = –5

Checking of Result

Given,

Now, LHS =

After substituting the value of x = –5 in this LHS, we get

Thus, LHS =

Now, RHS =

After substituting the value of x = –5 in this RHS, we get

Thus, RHS =

Thus, LHS = RHS Proved

Thus, x = –5 Answer

Question (4)

Solution

Given,

After cross multiplication, we get

5(x – 5) = 3(x – 3)

⇒ 5x – 25 = 3x – 9

After transposing –25 to RHS, we get

5x = 3x – 9 + 25

After transposing 3x to LHS, we get

5x – 3x = – 9 + 25

⇒ 2x = 16

After transposing 2 to RHS, we get

x = 16/2 = 8

⇒ x = 8 Answer

Checking of Result

Given,

We have LHS =

Now, after substituting the value of x = 8 in the LHS, we get

Thus, LHS = 1

Now, RHS =

Now, after substituting the value of x = 8 in the RHS, we get

Thus, RHS = 1

Thus, LHS = RHS Proved

Question (5)

Solution:

Given,

After transposing –t to LHS, we get

After cross multiplication, we get

3(13t – 18) = 2 × 12

⇒ 39t – 54 = 24

After transposing –54 to RHS, we get

39t = 24 + 54

⇒ 39t = 78

After transposing 39 to RHS, we get

t = 78/39 = 2

⇒ t = 2 Answer

Checking of Result

Given,

Now, LHS

After substituting the value of t = 2 in this LHS, we get

Thus, LHS =

Now, RHS =

After substituting the value of t = 2 in this LHS, we get

Thus, RHS

Thus, LHS = RHS Proved