## MP Board Class 8th Maths Solutions Chapter 2 Linear Equations in One Variable Ex 2.3

Solve the following equations and check your results.

Question 1.

3x = 2x + 18

Solution:

We have, 3x = 2x + 18

Transposing 2x to L.H.S., we get

3x – 2x = 18 ⇒ x = 18

Checking: L.H.S. = 3 × 18 = 54

R.H.S. = 2x + 18 = 2 × 18 + 18 = 36 + 18 = 54

Thus, L.H.S. = R.H.S.

Question 2.

5t – 3 = 3t – 5

Solution:

We have, 5t – 3 = 3t – 5

Transposing 3t to L.H.S., we get

5t – 3 – 3t = – 5

⇒ 2t – 3 = – 5

Transposing – 3 to R.H.S., we get

2t = -5 + 3

⇒ 2t = – 2

Dividing both sides by 2, we get

Checking : L.H.S. = 5t – 3 = 5 × (-1) – 3 = -5 – 3 = -8

R.H.S. = 3t – 5 = 3 × (-1) – 5 = -3 – 5 = -8

Thus, L.H.S. = R.H.S.

Question 3.

5x + 9 = 5 + 3x

Solution:

We have, 5x + 9 = 5 + 3x

Transposing 3x to L.H.S., we get

5x + 9 – 3x = 5

⇒ 2x + 9 = 5

Now, transposing 9 to R.H.S., we get

2x = 5 – 9 = 4 ⇒ 2x = – 4

Dividing both sides by 2, we get \(\frac{2 x}{2}=\frac{-4}{2}\)

Checking: L.H.S. = 5x + 9 = 5 × (-2) + 9 = -10 + 9 = -1

R.H.S. = 5 + 3x = 5 + 3 (-2) = 5 – 6 = – 1.

Thus, L.H.S. = R.H.S.

Question 4.

4z + 3 = 6 + 2z

Solution:

We have, 4z + 3 = 6 + 2z

Transposing 2z to L.H.S., we get

4z + 3-2z = 6 ⇒ 2z + 3 = 6

Transposing 3 to R.H.S., we get

2z = 6 – 3 ⇒ 2z = 3

Question 5.

2x – 1 = 14 – x

Solution:

We have, 2x -1 = 14 – x

Transposing – x to L.H.S., we get

2x – 1 + x = 14 ⇒ 3x – 1 = 14

Transposing – 1 to R.H.S., we get

3x = 14 + 1 ⇒ 3x = 15

Dividing both sides by 3, we get \(\frac{3 x}{3}=\frac{15}{3}\)

⇒ x = 15

Checking: L.H.S. = 2x – 1 = 2 × 5 – 1 = 10 – 1 = 9

R.H.S. = 14 – x = 14 – 5 = 9

Thus, L.H.S. = R.H.S.

Question 6.

8x + 4 = 3(x – 1) + 7

Solution:

We have, 8x + 4 = 3(x – 1) + 7

⇒ 8x + 4 = 3x – 3 + 7 ⇒ 8x + 4 = 3x + 4

Transposing 3x to L.H.S., we get

8x + 4 – 3x = 4 ⇒ 5x + 4 = 4

Transposing 4 to R.H.S., we get

⇒ 5x = 4 – 4 ⇒ 5x = 0

Dividing both sides by 5, we get

Checking: L.H.S. = 8x + 4 = 8 × 0 + 4 = 4

R.H.S. = 3(x – 1) + 7 = 3(0 – 1) + 7 = -3 + 7 = 4

Thus, L.H.S. = R.H.S.

Question 7.

x = \(\frac{4}{5}\)(x + 10)

Solution:

We have, x = \(\frac{4}{5}\)(x + 10)

Multiplying both sides by 5, we get

5x = 4(x + 10) ⇒ 5x = 4x + 40

Transposing 4x to L.H.S., we get 5x – 4x = 40 ⇒ x = 40

Checking : L.H.S. = x = 40

Thus, L.H.S. = R.H.S.

Question 8.

\(\frac{2 x}{3}+1=\frac{7 x}{15}+3\)

Solution:

Question 9.

\(2 y+\frac{5}{3}=\frac{26}{3}-y\)

Solution:

Question 10.

3m = 5m – \(\frac{8}{5}\)

Solution: