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Exercise 2.3 - Chapter 2 Linear Equations In One Variable class 8 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Solve and check result: 3x = 2x + 18

Answer:

3x = 2x + 18

On transposing 2x to L.H.S, we obtain

3x − 2x = 18

x = 18

L.H.S = 3x = 3 × 18 = 54

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

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 2:

Solve and check result: 5t − 3 = 3t − 5

Answer:

5t − 3 = 3t − 5

On transposing 3t to L.H.S and −3 to R.H.S, we obtain

5t − 3t = −5 − (−3)

2t = −2

On dividing both sides by 2, we obtain

t = −1

L.H.S = 5t − 3 = 5 × (−1) − 3 = −8

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

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 3:

Solve and check result: 5x + 9 = 5 + 3x

Answer:

5x + 9 = 5 + 3On transposing 3x to L.H.S and 9 to R.H.S, we obtain

5x − 3= 5 − 9

2x = −4

On dividing both sides by 2, we obtain

= −2

L.H.S = 5x + 9 = 5 × (−2) + 9 = −10 + 9 = −1

R.H.S = 5 + 3x = 5 + 3 × (−2) = 5 − 6 = −1

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 4:

Solve and check result: 4z + 3 = 6 + 2z

Answer:

4z + 3 = 6 + 2z

On transposing 2z to L.H.S and 3 to R.H.S, we obtain

4z − 2z = 6 − 3

2z = 3

Dividing both sides by 2, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2986/Chapter%202_html_m4c9f1935.gif

L.H.S = 4z + 3 = 4 ×https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2986/Chapter%202_html_501b900f.gif  + 3 = 6 + 3 = 9

R.H.S = 6 + 2z = 6 + 2 ×https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2986/Chapter%202_html_501b900f.gif  = 6 + 3 = 9

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 5:

Solve and check result: 2x − 1 = 14 − x

Answer:

2x − 1 = 14 − x

Transposing x to L.H.S and 1 to R.H.S, we obtain

2x + x = 14 + 1

3x = 15

Dividing both sides by 3, we obtain

x = 5

L.H.S = 2x − 1 = 2 × (5) − 1 = 10 − 1 = 9

R.H.S = 14 − x = 14 − 5 = 9

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 6:

Solve and check result: 8x + 4 = 3(x − 1) + 7

Answer:

8x + 4 = 3(− 1) + 7

8x + 4 = 3x − 3 + 7

Transposing 3x to L.H.S and 4 to R.H.S, we obtain

8− 3x = − 3 + 7 − 4

5x = − 7 + 7

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2990/Chapter%202_html_6a496db9.gif

L.H.S = 8x + 4 = 8 × (0) + 4 = 4

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

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 7:

Solve and check result: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2992/Chapter%202_html_32aca0e6.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2992/Chapter%202_html_32aca0e6.gif

Multiplying both sides by 5, we obtain

5x = 4(x + 10)

5x = 4x + 40

Transposing 4x to L.H.S, we obtain

5x − 4x = 40

x = 40

L.H.S = x = 40

R.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2992/Chapter%202_html_1f1e203.gif  = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2992/Chapter%202_html_mf7bccfb.gif

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 8:

Solve and check result: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_m13f98075.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_m13f98075.gif

Transposing https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_254673f5.gif  to L.H.S and 1 to R.H.S, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_53a04464.gif

Multiplying both sides by 5, we obtain

x = 10

L.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_3c6e6c0e.gifhttps://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_2e0d2c9c.gif

R.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2994/Chapter%202_html_m1f430cd9.gif

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 9:

Solve and check result: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_673a3015.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_673a3015.gif

Transposing y to L.H.S and https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_45970558.gif to R.H.S, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_m415218e.gif

Dividing both sides by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_m216b325a.gif

L.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_m1ce0d501.gif https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_6b8a0633.gif

R.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2996/Chapter%202_html_19eea150.gif

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Question 10:

Solve and check result: https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_m64d56f11.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_m64d56f11.gif

Transposing 5m to L.H.S, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_mc3db258.gif

Dividing both sides by −2, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_4dd7717b.gif

L.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_m4619e99e.gif  https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_m4948efb.gif

R.H.S = https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/65/2997/Chapter%202_html_m3a36ea94.gif

L.H.S. = R.H.S.

Hence, the result obtained above is correct.

Also Read : Exercise-2.4-Chapter-2-Linear-Equations-In-One-Variable-class-8-ncert-solutions-Maths

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