NCERT Solutions Class 8 Mathematics Linear Equations in One Variable Ex 2.3

Solve the following equations and check your results.

Question: 1. 3𝓍 = 2𝓍 + 18

Answer : 3𝓍 = 2𝓍 + 18

⇒ 3𝓍 – 2𝓍 = 18

⇒ 𝓍 = 18

To Check:

3𝓍 = 2𝓍 + 18

⇒ 3 x 18 = 2 x 18 + 18

⇒ 54 = 36 +18

⇒ 54 = 54

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 2. 5t – 3 = 3t -5

Answer : 5t – 3 = 3t – 5

⇒ 5t – 3t = -5 + 3

⇒ 2t = -2

⇒ t = -1 (Divide both sides by 2)

To Check:

5t – 3 = 3t – 5

⇒ 5 x (-1) – 3 = 3 x (-1) – 5

⇒ -5 -3 = -3 – 5

⇒ -8 = -8

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 3. 5𝓍 + 9 = 5 + 3𝓍

Answer : 5𝓍 + 9 = 5 + 3𝓍

⇒ 5𝓍 – 3𝓍 = 5 – 9

⇒ 2𝓍 = -4

⇒ 𝓍 = -2

To Check :

5𝓍 + 9 = 5 + 3𝓍

⇒ 5 x (-2) + 9 = 5 + 3 x (-2)

⇒ -10 + 9 = 5 – 6

⇒ -1 = -1

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 4. 4z + 3 = 6 + 2z

Answer : 4z + 3 = 6 + 2z

⇒ 4z – 2z = 6 – 3

⇒ 2z = 3

⇒ z = ³⁄₂

To Check:

4z + 3 = 6 + 2z

⇒ 4 x (³⁄₂) + 3 = 6 + 2 x (³⁄₂)

⇒ (2 x 3) + 3 = 6 + 3

⇒ 9 = 9

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 5. 2𝓍 – 1 = 14 – 𝓍

Answer : 2𝓍 – 1 = 14 – 𝓍

⇒ 2𝓍 + 𝓍 = 14 + 1

⇒ 3𝓍 = 15

⇒ 𝓍 = 5 (divide both side by 3)

To Check:

2𝓍 – 1 = 14 – 𝓍

⇒ 2 x 5 – 1 = 14 – 5

⇒ 9 = 9

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 6. 8𝓍 + 4 = 3(𝓍 – 1) + 7

Answer : 8𝓍 + 4 = 3(𝓍 – 1) + 7

⇒ 8𝓍 + 4 = 3𝓍 – 3 + 7

⇒ 8𝓍 – 3𝓍 = + 4 – 4

⇒ 5𝓍 = 0

⇒ 𝓍 = 0

To Check:

8𝓍 + 4 = 3(𝓍 – 1) + 7

⇒ 8 x 0 + 4 = 3(0 – 1) + 7

⇒ 0 + 4 = 3 x 0 – 3 x 1 + 7

⇒ 4 = 0 – 3 + 7

⇒ 4 = 4

⇒ L.H.S. = R.H.S.

Hence, it is correct.

Question: 7. 𝓍 = ⁴⁄₅(𝓍 + 10)

Answer : 𝓍 = ⁴⁄₅(𝓍 + 10)

5𝓍 = 4(𝓍 + 10)

5𝓍 = 4𝓍 + 40

5𝓍 – 4𝓍 = 40

𝓍 = 40

To Check:

𝓍 = ⁴⁄₅(𝓍 + 10)

40 = ⁴⁄₅(40 + 10)

40 = ⁴⁄₅(50)

40 = 4 (10)

40 = 40

⇒ L.H.S. = R.H.S.

Hence, it is correct.