These NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.3 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Exercise 4.3
Question 1.
Solve the following equations:
(a) 2y + \(\frac{5}{2}=\frac{37}{2}\)
(b) 5t + 28 = 10
(c) \(\frac{\mathrm{a}}{5}\) + 3 = 2
(d) \(\frac{\mathrm{q}}{4}\) + 7 = 5
(e) \(\frac{5}{2}\) x = -10
(f) \(\frac{5}{2}\) x = \(\frac{25}{4}\)
(g) 7m + \(\frac{19}{2}\) = 13
(h) 6z + 10 = -2
(i) \(\frac{31}{2}=\frac{2}{3}\)
(j) \(\frac{2 \mathrm{~b}}{3}\) – 5 = 3
Answer:
(a) we have
2y + \(\frac{5}{2}=\frac{37}{2}\)
Transposing \(\frac{5}{2}\) from L.H.S to R.H.S
2y = \(\frac{37}{2}-\frac{5}{2}\)
2y = \(\frac{37-5}{2}\)
2y = \(\frac{32}{2}\)
2y = 16.
(b) we have
5t + 28 = 10
Transposing 28 from L.H.S to R.H.S
5t = 10 – 28
5t = – 18
Dividing both sides by 5, we get
\(\frac{5 \mathrm{t}}{5}=\frac{-18}{5}\)
t = \(\frac{-18}{5}\)
The solution is t = \(\frac{-18}{5}\) or -3 \(\frac{3}{5}\)
Dividing both sides by 2, we get
\(\frac{2 y}{2}=\frac{16}{2}\)
y = 8
y = 8 is the required solution.
(c) we have a
\(\frac{\mathrm{a}}{5}\) + 3 = 2
Transposing 3 from L.H.S to R.H.S
\(\frac{\mathrm{a}}{5}\) = 2 – 3
\(\frac{\mathrm{a}}{5}\) = -1
Multiplying both sides by 5, we get
\(\frac{\mathrm{a} \times 5}{5}\) = -1 x 5
a = – 5
The solution is a = – 5.
(d) We have
\(\frac{\mathrm{q}}{4}\) + 7 = 5
Transposing 7 to R.H.S
\(\frac{\mathrm{q}}{4}\) = 5 – 7
\(\frac{\mathrm{q}}{4}\) = -2
Multiplying both sides by 4, we get
\(\frac{\mathrm{q}}{4}\) × 4 = – 2 × (4)
q = -8
The solution is q = – 8.
(e) We have
\(\frac{5}{2}\) x = – 10
Multiplying both sides by 2, we get
\(\frac{5}{2}\) x x 2 = -10 × 2
5x = – 20
Dividing both sides by 5, we get
\(\frac{5 x}{5}=\frac{-20}{5}\)
The solution is x = – 4.
(f) We have
\(\frac{5}{2}\) x = \(\frac{25}{4}\)
Multiplying both sides by 2, we get
\(\frac{5}{2}\) x × 2 = \(\frac{25}{4}\) × 2
5x = \(\frac{25}{2}\)
Dividing both sides by 5, we get
\(\frac{5 x}{5}=\frac{25}{2 \times 5}\)
x = \(\frac{5}{2}\)
The solution is x= \(\frac{5}{2}\) or x = 2 \(\frac{1}{2}\).
(g) We have
7m + \(\frac{19}{2}\) = 13
Transposing \(\frac{19}{2}\) to R.H.S
7m = 13 – \(\frac{19}{2}\)
7m = \(\frac{26-19}{2}\)
7m = \(\frac{7}{2}\)
(h) We have
6z + 10 = – 2
Transposing 10 to R.H.S
6z = – 2 – 10
6z = – 12
Dividing both sides by 6, we get
\(\frac{6 z}{6}=\frac{-12}{6}\)
z = – 2
The solution is z = – 2.
Dividing both sides by 7, we get
\(\frac{7 \mathrm{~m}}{7}=\frac{7}{2 \times 7}\)
m = \(\frac{1}{2}\)
The solution is m = \(\frac{1}{2}\) .
(i) We have
\(\frac{31}{2}=\frac{2}{3}\)
Multiplying both sides by 2, we get
\(\frac{31}{2}\) x 2 = \(\frac{2}{3}\) x 2
31 = \(\frac{4}{3}\)
Dividing both sides by 3, we get
\(\frac{31}{3}=\frac{4}{3 \times 3}\)
1 = \(\frac{4}{9}\)
The solution is 1 = \(\frac{4}{9}\)
(j) We have
\(\frac{2 \mathrm{~b}}{3}\) – 5 = 3
Transposing – 5 to R.H.S
\(\frac{2 \mathrm{~b}}{3}\) = 3 + 5
\(\frac{2 \mathrm{~b}}{3}\) = 8
Multiplying both sides by 3, we get
\(\frac{2 \mathrm{~b}}{3}\) × 3 = 8 × 3
2b = 24
Dividing both sides by 2, we get
\(\frac{2 b}{2}=\frac{24}{2}\)
b = 12
The solution is b = 12.
Question 2.
Solve the following equations:
(a) 2(x + 4) = 12
(b) 3(n – 5) = 21
(c) 3(n – 5) = – 21
(d) – 4(2 + x) = 8
(e) 4(2 – x) = 8
Answer:
(a) 2(x + 4) = 12
Dividing both sides by 2, we get
\(\frac{2(x+4)}{2}=\frac{12}{2}\) ⇒ x + 4 = 6
Transposing 4 to R.H.S
x = 6 – 4 = 2
(b) 3(n – 5) = 21
Dividing both sides by 3, we get
\(\frac{3(n-5)}{3}=\frac{21}{3}\)
⇒ n – 5 = 7
Transposing – 5 to R.H.S
n = 7 + 5 = 12
(c) 3(n – 5) = -21
Dividing both sides by 3, we get
\(\frac{3(n-5)}{3}=\frac{-21}{3}\)
⇒ n – 5 = -7
Transposing – 5 to R.H.S
n = -7 + 5 = -2
(d) – 4(2 + x) =8
Dividing both sides by -4, we get
\(\frac{-4(2+x)}{-4}=\frac{8}{-4}\)
⇒ 2 + x = – 2
Transposing 2 to R.H.S
x = -2 -2 = -4
(e) 4(2 – x) = 8
Dividing both sides by 4, we get 4(2-x) _ 8
\(\frac{4(2-\mathrm{x})}{4}=\frac{8}{4}\)
⇒ 2 – x = 2
Transposing 2 to R.H.S
-x = 2 – 2 = 0
Multiplying both sides by (- 1), we get
-x × (-1) = 0 × (- 1)
x = 0
Question 3.
Solve the following equations:
(a) 4 = 5(p – 2)
(b) – 4 = 5(p – 2)
(c) 16 = 4 + 3(t + 2)
(d) 4 + 5(p – 1) = 34
(e) 0 = 16 + 4(m – 6)
Answer:
(a) 4 = 5 (p – 2)
Interchanging the sides, we get 5 ( p – 2) =4
Dividing both sides by 5, we get
\(\frac{5(p-2)}{5}=\frac{4}{5}\)
⇒ p – 2 = \(\frac{4}{5}\)
Transposing -2 to R.H.S
p = \(\frac{4}{5}\) + 2
= \(\frac{4+10}{5}=\frac{14}{5}\) = 2\(\frac{4}{5}\)
(b) – 4 = 5(p – 2)
Interchanging the sides, we get }
5 ( p – 2) = -4
Dividing both sides by 5, we get
\(\frac{5(p-2)}{5}=\frac{-4}{5}\)
p – 2 = \(\frac{-4}{5}\)
Transposing – 2 to R.H.S
p = \(\frac{-4}{5}\) + 2 = \(\frac{-4+10}{5}\)
= \(\frac{6}{5}\) = 1\(\frac{1}{5}\)
(c) 16 = 4 + 3(t + 2)
Interchanging the sides, we get 4 + 3 (t + 2) = 16
Transposing 4 to R.H.S
3(t + 2) – 16 – 4 = 12
Dividing both sides by 3, we get
\(\frac{3(t+2)}{3}=\frac{12}{3}\)
⇒ t + 2 = 4
Transposing 2 to R.H.S
t = 4 – 2 = 2
(d) 4 + 5 (p – 1) = 34
Transposing 4 to R.H.S
5 (p – 1) = 34 – 4 = 3
Dividing both sides by 5, we get
\(\frac{5(\mathrm{p}-1)}{5}=\frac{30}{5}\)
p – 1 = 6
Transposing -1 to R.H.S
p = 6 + 1 = 7
(e) 0 = 16 + 4(m – 6)
Interchanging the sides we get
16 + 4(m – 6) = 0
Transposing 16 to R.H.S
4(m – 6) = 0 – 16 = – 16
Dividing both sides by 4 we get
\(\frac{4(\mathrm{~m}-6)}{4}=\frac{-16}{4}\)
⇒ m – 6 = – 4
Transposing – 6 to R.H.S
m = -4 + 6 = 2
Question 4.
(a) Construct 3 equations starting with x = 2
(b) Construct 3 equations starting with x = – 2
Answer:
(a) Starting with x = 2
(1) Multiplying both sides by 3, we get
3x = 6
Subtracting 7 from both sides, we get
3x – 7 = 6 – 7
3x – 7 = – 1
(2) x = 2
Adding 5 on both sides, we get
x + 5 = 2 + 5
x + 5 = 7
Multiplying both sides by 4, we get
4(x + 5) = 7 × 4
4 (x + 5) = 28
(b) Starting with x = – 2
(1) x = – 2
Adding 11 to both sides, we get
x + 11 = – 2 + 11
x + 11 = 9
(2) x = – 2
Multiplying both sides by 5, we get
5x = – 10
Adding 3 on both sides, we get
5x + 3 = – 10 + 3
5x + 3 = – 7
(3) x = 2
Dividing both sides by 5, we get
\(\frac{x}{5}=\frac{2}{5}\)
Subtracting 2 from both sides, we get
\(\frac{\mathrm{x}}{5}\) – 2 = \(\frac{2}{5}\) -2
\(\frac{\mathrm{x}}{5}\) – 2 = \(\frac{2-10}{5}\)
\(\frac{\mathrm{x}}{5}\) – 2 = \(\frac{-8}{5}\)
(3) x = – 2
Dividing both sides by 7, we get
\(\frac{x}{7}=\frac{-2}{7}\)
Add 3 on both sides, we get
\(\frac{\mathrm{X}}{7}\) + 3 = \(\frac{-2}{7}\) + 3
= \(\frac{-2+21}{7}\)
\(\frac{\mathrm{X}}{7}\) + 3 = \(\frac{19}{7}\)