# Simple Equations

## Exercise 4.1

Question 1: Complete the last column of the table.

S. No.EquationValueEquation is satisfied
(Yes/No)
(a)x + 3 = 0x = 3
(b)x + 3 = 0x = 0
(c)x + 3 = 0x = -3
(d)x – 7 = 1x = 7
(e)x – 7 = 1x = 8
(f)5x = 25x = 5
(g)5x = 25x = -5
(h)m/3 = 2m = - 6
(i)m/3 = 2m = 0
(j)m/3 = 2m = 6

Answer: a → No, b → No, c → Yes, d → No, e → yes, f → Yes, g → No, h → No, i → no, j → yes

Question 2: Check whether the value given in the brackets is a solution to the given equation or not:

(a) n + 5 = 19 (n = 1)

Answer: n + 5 = 19

Or, n = 19 – 5 = 14

Hence, the value in the bracket is not correct.

(b) 7n + 5 = 19 (n = – 2)

Answer: 7n + 5 = 19

Or, 7n = 19 – 5 = 14

Or, n = 14 ÷ 7 = 2

Hence, the value in the bracket is not correct.

(c) 7n + 5 = 19 (n = 2)

Answer: 7n + 5 = 19

Or, 7n = 19 – 5 = 14

Or, n = 14 ÷ 7 = 2

Hence, the value in the bracket is correct.

(d) 4p – 3 = 13 (p = 1)

Answer: 4p – 3 = 13

Or, 4p = 13 + 3 = 16

Or, p = 16 ÷ 4 = 4

Hence, the value in the bracket is not correct.

(e) 4p – 3 = 13 (p = – 4)

Answer: 4p – 3 = 13

Or, 4p = 13 + 3 = 16

Or, p = 16 ÷ 4 = 4

Hence, the value in the bracket is not correct.

(f) 4p – 3 = 13 (p = 0)

Answer: 4p – 3 = 13

Or, 4p = 13 + 3 = 16

Or, p = 16 ÷ 4 = 4

Hence, the value in the bracket is not correct.

Question 3: Solve the following equations by trial and error method:

(a) 5p + 2 = 17

Answer: Let us assume, p = 1

Then, 5p + 2 = 5 xx 1 + 2 = 5 + 2 = 7

Let us assume p = 2

Then, 5p + 2 = 5 xx 2 + 2 = 10 + 2 = 12

Let us now assume p = 3

Then, 5p + 2 = 5 xx 3 + 2 = 15 + 2 = 17

Hence, p = 3 is the correct value.

(b) 3m – 14 = 4

Answer: Let us assume, m = 2

Then, 3m – 14 = 3 xx 2 – 14 = 6 – 14 = - 11

Let us assume, m = 4

Then, 3m – 14 = 3 xx 4 – 14 = 12 – 14 = - 2

Let us now assume, m = 6

Then, 3m – 14 = 3 xx 6 – 14 = 18 0 14 = 4

Hence, m = 6 is the correct value.

Question 4: Write equations for the following statements:

(a) The sum of numbers x and 4 is 9.

Answer: x + 4 = 9

(b) 2 subtracted from y is 8.

Answer: y – 2 = 8

(c) Ten times a is 70.

Answer: 10a = 70

(d) The number b divided by 5 gives 6.

Answer: b/5 = 6

(e) Three-fourth of t is 15.

Answer: (3/4)t = 15

(f) Seven times m plus 7 gets you 77.

Answer: 7m +7 = 77

(g) One-fourth of a number x minus 4 gives 4.

Answer: (x/4) – 4 = 4

(h) If you take away 6 from 6 times y, you get 60.

Answer: 6y – 6 = 60

(i) If you add 3 to one-third of z, you get 30.

Answer: (z/3) + 3 = 30

Question 5: Write the following equations in statement forms:

(a) p + 4 = 15

Answer: Sum of p and 4 is 15.

(b) m – 7 = 3

Answer: When is 7 is subtracted from m, we get 3.

(c) 2m = 7

Answer: Two times m is 7.

(d) m/5 = 3

Answer: One fifth of m is 3.

(e) (3m)/(5) = 6

Answer: Three fifth of m is 6.

(f) 3p + 4 = 25

Answer: When 4 is added to three times of p, we get 25.

(g) 4p – 2 = 18

Answer: When 2 is subtracted from 4 times p, we get 18.

(h) (p/2) + 2 = 8

Answer: When 2 is added to half of p, we get 8.

Question 6: Set up an equation in the following cases:

(a) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)

Answer: 5m + 7 = 37

(b) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)

Answer: 3y + 4 = 49

(c) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)

Answer: 2l + 7 = 87

(d) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).

Answer: 4b = 180°