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Exercise 4.2 - Chapter 4 Simple Equations class 7 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Give first the step you will use to separate the variable and then solve the equation:

(a) x + 1 = 0 (b) x + 1 = 0 (c) x − 1 = 5

(d) x + 6 = 2 (e) y − 4 = − 7 (f) − 4 = 4

(g) y + 4 = 4 (h) y + 4 = − 4

Answer:

(a) x − 1 = 0

Adding 1 to both sides of the given equation, we obtain

− 1 + 1 = 0 + 1

x = 1

(b) x + 1 = 0

Subtracting 1 from both sides of the given equation, we obtain

x + 1 − 1 = 0 − 1

x = −1

(c) − 1 = 5

Adding 1 to both sides of the given equation, we obtain

x − 1 + 1 = 5 + 1

x = 6

(d) x + 6 = 2

Subtracting 6 from both sides of the given equation, we obtain

x + 6 − 6 = 2 − 6

x = −4

(e) y − 4 = −7

Adding 4 to both sides of the given equation, we obtain

y − 4 + 4 = − 7 + 4

y = −3

(f) y − 4 = 4

Adding 4 to both sides of the given equation, we obtain

y − 4 + 4 = 4 + 4

y = 8

(g) y + 4 = 4

Subtracting 4 from both sides of the given equation, we obtain

y + 4 − 4 = 4 − 4

y = 0

(h) y + 4 = −4

Subtracting 4 from both sides of the given equation, we obtain

y + 4 − 4 = − 4 − 4

y = −8

Question 2:

Give first the step you will use to separate the variable and then solve the equation:

(a) 3= 42 (b) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_md82059d.gif  (c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m49475470.gif

(d) 4x = 25 (e) 8y = 36 (f) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_231ef9f3.gif

(g) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_2d160d2e.gif  (h) 20= − 10

Answer:

(a) 3l = 42

Dividing both sides of the given equation by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_3e0bd5a0.gif

l = 14

(b) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m5d7326bc.gif

Multiplying both sides of the given equation by 2, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m621c7308.gif

b = 12

(c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m3028fb0f.gif

Multiplying both sides of the given equation by 7, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_20457a0c.gif

p = 28

(d) 4x = 25

Dividing both sides of the given equation by 4, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_549b0f26.gif

x = https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m3c47c6d4.gif

(e) 8y = 36

Dividing both sides of the given equation by 8, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_65023d5f.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_mdde0fd6.gif

(f) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m72a6a6ee.gif

Multiplying both sides of the given equation by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m637fc180.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_19bae4c5.gif

(g) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_705b7b80.gif

Multiplying both sides of the given equation by 5, we obtain https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m313aeaa.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m34523972.gif

(h) 20t = −10

Dividing both sides of the given equation by 20, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1876/Chapter%204_html_m5af42111.gif

Question 3:

Give the steps you will use to separate the variable and then solve the equation:

(a) 3n − 2 = 46 (b) 5m + 7 = 17 (c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_567803b5.gif

(d) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_59f003ca.gif

Answer:

(a) 3n − 2 = 46

Adding 2 to both sides of the given equation, we obtain

3n − 2 + 2 = 46 + 2

3n = 48

Dividing both sides of the given equation by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_m7210aded.gif

n = 16

(b) 5m + 7 = 17

Subtracting 7 from both sides of the given equation, we obtain

5m + 7 − 7 = 17 − 7

5m = 10

Dividing both sides of the given equation by 5, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_36a4ab2b.gif

(c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_153d7afb.gif

Multiplying both sides of the given equation by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_5664ba9.gif

Dividing both sides of the given equation by 20, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_6ef15847.gif

(d)https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_m14e24310.gif

Multiplying both sides of the given equation by 10, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_368f614e.gif

Dividing both sides of the given equation by 3, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1880/Chapter%204_html_m4a99e4c0.gif

p = 20

Question 4:

Solve the following equations:

(a) 10p = 100 (b) 10p + 10 = 100 (c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m5aa9408b.gif

(d) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m14e3e927.gif  (e) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m7d91a29d.gif  (f) 3s = − 9

(g) 3s + 12 = 0 (h) 3s = 0 (i) 2q = 6

(j) 2q − 6 = 0 (k) 2q + 6 = 0 (l) 2q + 6 = 12

Answer:

(a) 10 p = 100

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_7492c501.gif

(b) 10 p + 10 = 100

10 + 10 − 10 = 100 − 10

10 p = 90

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m8728977.gif

(c) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m5aa9408b.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_69ef266d.gif

(d) https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m70f7a891.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_4d7cb41d.gif

(e)

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m6604fe90.gif

(f) 3 s = −9

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m77b6a3de.gif

(g) 3 s + 12 = 0

s + 12 − 12= 0 − 12

s = −12

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m7411bd40.gif

(h) 3 s = 0

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m24ebe707.gif

(i) 2q = 6

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m24d8a470.gif

(j) 2q − 6 = 0

2q − 6 + 6 = 0 + 6

2q = 6

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m24d8a470.gif

(k) 2q + 6 = 0

2q + 6 − 6 = 0 − 6

2q = −6

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m2dd45040.gif

(l) 2q + 6 = 12

2q + 6 − 6 = 12 − 6

2q = 6

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/34/1883/Chapter%204_html_m24d8a470.gif

Also Read : Exercise-4.3-Chapter-4-Simple-Equations-class-7-ncert-solutions-Maths

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