Linear Equations in One Variable - 8th math

Solve the following equations and check your results

Question (1) 3x = 2 x + 18

Solution: Given,

3x = 2x + 18

After transposing 2x to LHS, we get

3x - 2x=18

⇒ x = 18 Answer

Checking of result of Result

Given equation is 3x = 2x + 18

After substituting the value of x in LHS and RHS we get:

3x = 2 × 18 + 18

⇒ 3 × 18 = 36 + 18

⇒ 3 × 18 = 54

⇒ 54 = 54

Thus, LHS = RHS

Question (2) 5t – 3 = 3t – 5

Solution:

Given, 5t – 3 = 3t – 5

After transposing 3t to LHS we get:

5t – 3 – 3t = –5

After transposing –3 to RHS we get

5t – 3t =–5 + 3

⇒ 2t = –2

After transposing 2 to RHS, we get

⇒ t = –1 Answer

Checking of Result

Given,

5t – 3 = 3t – 5

RHS = 3t – 5

After substituting the value of t = –1 which is calculated in the solution in RHS, we get

RHS = 3 × (–1) – 5

= –3 – 5

⇒ RHS = –8

LHS = 5t – 3

After substituting the value of t = –1 which is calculated in the solution in LHS, we get

LHS = 5(–1) – 3

= –5 – 3

⇒ LHS = –8

Thus, LHS = RHS proved

Question (3) 5x + 9 = 5 + 3x

Solution:

Given, 5x + 9 = 5 + 3x

After transposing 9 to RHS, we get

⇒ 5x = 5 + 3x – 9

And, after transposing 3x to LHS, we get

⇒ 5x – 3x = 5 – 9

⇒ 2x = –4

After dividing both sides by 2, we get

⇒ 2x/2 = –4/2

⇒ x = –2 Answer

CHECKING OF RESULT:

Given, 5x + 9 = 5 + 3x

LHS = 5x + 9

After substituting the value of x = –2, we get

LHS = 5 (–2) + 9

= –10 + 9

⇒ LHS = –1

Now, RHS = 5 + 3x

After substituting the value of x = –2, we get

LHS = 5 + 3 (–2)

= 5 + (–6)

= 5 – 6

⇒ LHS = –1

Thus, LHS = RHS Proved

Question (4) 4x + 3 = 6 + 2x

Solution:

Given, 4x + 3 = 6 + 2x

After transposing 3 to RHS, we get

4x = 6 + 2x – 3

Now, after transposing 2x to LHS, we get

4x – 2x = 6 – 3

⇒ 2x = 3

After dividing both sides by 2 we get

⇒ (2x)/2 = 3/2

⇒ x = 3/2 Answer

CHECKING OF RESULT:

Given, 4x + 3 = 6 + 2x

LHS = 4x + 3

Substituting the value of x = 3/2 in LHS we get

= 4 × 3/2 + 3

= 2 × 3 + 3

= 6 + 3 = 9

⇒ LHS = 9

Now, RHS = 6 + 2x

Substituting the value of x = 3/2 in RHS we get

= 6 + 2 × 3/2

= 6 + 3 = 9

⇒ RHS = 9

Thus, LHS = RHS proved

Question (5) 2x – 1 = 14 – x

Solution:

Given, 2x – 1 = 14 – x

After transposing –1 to RHS, we get

2x = 14 – x + 1

After transposing –x to LHS, we get

2x + x = 14 + 1

⇒ 3x = 15

After transposing 3 to RHS, we get

x = 15/3 = 5

Thus, x = 5 Answer

CHECKING OF RESULT:

Given, 2x – 1 = 14 – x

Now, LHS =2x – 1

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

2 × 5 –1

= 10 – 1

Thus, LHS = 9

Now, RHS = 14 – x

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

= 14 – 5

⇒ RHS= 9

Thus, LHS = RHS proved