# 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:

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

Answer: n + 5 = 19
Or, n = 19 – 5 = 14
Hence, the value in the bracket is not correct.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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:

1. 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.
2. 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:

1. The sum of numbers x and 4 is 9.

Answer: x + 4 = 9
2. 2 subtracted from y is 8.

Answer: y – 2 = 8
3. Ten times a is 70.

Answer: 10a = 70
4. The number b divided by 5 gives 6.

Answer: b/5 = 6
5. Three-fourth of t is 15.

Answer: (3/4)t = 15
6. Seven times m plus 7 gets you 77.

Answer: 7m +7 = 77
7. One-fourth of a number x minus 4 gives 4.

Answer: (x/4) – 4 = 4
8. If you take away 6 from 6 times y, you get 60.

Answer: 6y – 6 = 60
9. If you add 3 to one-third of z, you get 30.

Answer: (z/3) + 3 = 30

10. Question 5: Write the following equations in statement forms:

1. p + 4 = 15

Answer: Sum of p and 4 is 15.
2. m – 7 = 3

Answer: When is 7 is subtracted from m, we get 3.
3. 2m = 7

Answer: Two times m is 7.
4. m/5 = 3

Answer: One fifth of m is 3.
5. (3m)/(5) = 6

Answer: Three fifth of m is 6.
6. 3p + 4 = 25

Answer: When 4 is added to three times of p, we get 25.
7. 4p – 2 = 18

Answer: When 2 is subtracted from 4 times p, we get 18.
8. (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:

1. 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
2. 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
3. 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
4. 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°