Simple Equations
Exercise 4.1
1). Complete the last column of the table.
Answer:
| S No. | Equation | Value | Say, whether the Equation is satisfied (Yes/No) |
| i | x + 3 = 0 | x = 3 | No |
| ii | x + 3 = 0 | x = 0 | No |
| iii | x + 3 = 0 | x = -3 | Yes |
| iv | x – 7 = 1 | x = 7 | No |
| v | x – 7 = 1 | x = 8 | Yes |
| vi | 5x = 25 | x = 0 | No |
| vii | 5x = 25 | x = 5 | Yes |
| viii | 5x = 25 | x = -5 | No |
| ix | m/3 = 2 | m = -6 | No |
| x | m/3 = 2 | m = 0 | No |
| xi | m/3 = 2 | m = 6 | Yes |
i). x + 3 = 0
put x = 3 in L.H.S
L.H.S = 3 + 3 = 6
L.H.S ≠ R.H.S
x = 3 is not the solution.
ii). x + 3 = 0
put x = 0 in L.H.S
L.H.S = 0 + 3 = 3
L.H.S ≠ R.H.S
x = 0 is not the solution.
iii). x + 3 = 0
put x = -3 in L.H.S
L.H.S = -3 + 3 = 0
L.H.S = R.H.S
x = -3 is the solution.
iv). x – 7 = 1
put x = 7 in L.H.S
L.H.S = 7 – 7 = 0
L.H.S ≠ R.H.S
x = 7 is not the solution.
v). x – 7 = 1
put x = 8 in L.H.S
L.H.S = 8 – 7 = 1
L.H.S = R.H.S
x = 8 is the solution.
vi). 5x = 25
put x = 0 in L.H.S
L.H.S = 5 X 0 = 0
L.H.S ≠ R.H.S
x = 0 is not the solution.
vii). 5x = 25
put x = 5 in L.H.S
L.H.S = 5 X 5 = 25
L.H.S = R.H.S
x = 5 is the solution.
viii). 5x = 25
put x = -5 in L.H.S
L.H.S = 5 X -5 = -25
L.H.S ≠ R.H.S
x = -5 is not the solution.
ix). m/3 = 2
put m = -6 in L.H.S
L.H.S = -6/3 = -2
L.H.S ≠ R.H.S
m = -6 is not the solution.
x). m/3 = 2
put m = 0 in L.H.S
L.H.S = 0/3 = 0
L.H.S ≠ R.H.S
m = 0 is not the solution.
xi). m/3 = 2
put m = 6 in L.H.S
L.H.S = 6/3 = 2
L.H.S = R.H.S
m = 6 is the solution.
2). Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1) (b) 7n + 5 = 19 (n = – 2)
(c) 7n + 5 = 19 (n = 2) (d) 4p – 3 = 13 (p = 1)
(e) 4p – 3 = 13 (p = – 4) (f) 4p – 3 = 13 (p = 0)
Solutions:
(a) n + 5 = 19 (n = 1)
L.H.S = n + 5 = 1 + 5 = 6
R.H.S = 19
L.H.S ≠ R.H.S
Therefore, n =1 is not the solution of the given equation.
(b) 7n + 5 = 19 (n = – 2)
L.H.S = 7n + 5 = 7(-2) + 5
= -14 + 5
= -9
R.H.S = 19
L.H.S ≠ R.H.S
Therefore, n = -2 is not the solution of the given equation.
(c) 7n + 5 = 19 (n = 2)
L.H.S = 7n + 5 = 7(2) + 5
= 14 + 5
= 19
R.H.S = 19
L.H.S = R.H.S
Therefore, n = 2 is the solution of the given equation.
(d) 4p – 3 = 13 (p = 1)
L.H.S = 4p – 3
= 4(1) – 3
= 4 – 3
= 1
R.H.S = 13
L.H.S ≠ R.H.S
Therefore, p = 1 is not the solution of the given equation.
(e) 4p – 3 = 13 (p = – 4)
L.H.S = 4p – 3
= 4(-4) -3
= -16- 3
= -19
R.H.S = 13
L.H.S ≠ R.H.S
Therefore, p = -4 is not the solution of the given equation.
(f) 4p – 3 = 13 (p = 0)
L.H.S = 4p – 3
= 4(0) -3
= 0- 3
= -3
R.H.S = 13
L.H.S ≠ R.H.S
Therefore, p = 0 is not the solution of the given equation.
3). Solve the following equations by trial and error method:
(i) 5p + 2 = 17 (ii) 3m – 14 = 4
Solution:
(i) 5p + 2 = 17
Let p = 1
L.H.S = 5p + 2
= 5(1) + 2
= 5 + 2
= 7
R.H.S = 17
L.H.S ≠ R.H.S
Let p = 2
L.H.S = 5p + 2
= 5(2) + 2
= 10 + 2
= 12
R.H.S = 17
L.H.S ≠ R.H.S
Let p = 3
L.H.S = 5p + 2
= 5(3) + 2
= 15 + 2
= 17
R.H.S = 17
L.H.S = R.H.S
p = 3 is the solution of the given equation.
(ii) 3m – 14 = 4
Let m = 1
L.H.S = 3m – 14
= 3(1) – 14
= 3 – 14
= -11
R.H.S = 4
L.H.S ≠ R.H.S
Let m = 2
L.H.S = 3m – 14
= 3(2) – 14
= 6 – 14
= -8
R.H.S = 4
L.H.S ≠ R.H.S
Let m = 3
L.H.S = 3m – 14
= 3(3) – 14
= 9 – 14
= -5
R.H.S = 4
L.H.S ≠ R.H.S
Let m = 4
L.H.S = 3m – 14
= 3(4) – 14
= 12 – 14
= -2
R.H.S = 4
L.H.S ≠ R.H.S
Let m = 5
L.H.S = 3m – 14
= 3(5) – 14
= 15 – 14
= 1
R.H.S = 4
L.H.S ≠ R.H.S
Let m = 6
L.H.S = 3m – 14
= 3(6) – 14
= 18 – 14
= 4
R.H.S = 4
L.H.S = R.H.S
m = 6 is the solution of the given equation.
4). Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
x + 4 = 9
(ii) 2 subtracted from y is 8.
y – 2 = 8
(iii) Ten times a is 70.
10a = 70
(iv) The number b divided by 5 gives 6.
b/5 = 6
(v) Three-fourth of t is 15.
¾ X t = 15
(vi) Seven times m plus 7 gets you 77.
7m + 7 = 77
(vii) One-fourth of a number x minus 4 gives 4.
¼ X x -4 = 4
(viii) If you take away 6 from 6 times y, you get 60.
6y – 6 = 60
(ix) If you add 3 to one-third of z, you get 30.
1/3 X z + 3 = 30
5). Write the following equations in statement forms:
(i) p + 4 = 15 (ii) m – 7 = 3 (iii) 2m = 7 (iv)m/5 = 3
(v)3m/5= 6 (vi) 3p + 4 = 25 (vii) 4p – 2 = 18
(viii)p/2 + 2 = 8
Answer:
(i) p + 4 = 15
The Sum of a number p and 4 is 15.
(ii) m – 7 = 3
7 subtracted from a number m gives 3.
(iii) 2m = 7
Two times m is 7.
(iv)m/5 = 3
m divided by 5 is 3.
(v)3m/5= 6
3 times of m divided by 5 gives 6.
(vi) 3p + 4 = 25
The sum of 3 times of a number p and 4 is 25.
(vii) 4p – 2 = 18
The difference of 4 times of a p and 2 is 18.
(viii)p/2 + 2 = 8
The sum of half of p and 2 gives 8.
6). Set up an equation in the following cases:
(i) 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.)
Number of marbles with Irfan = 37
Let the number of marbles with Parmit be m
The required equation is
5m + 7 = 37
(ii) 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.)
Let the age of Laxmi be y years
Age of Laxmi’s father = 49
3y + 4 = 49
(iii) 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.)
Let the lowest score be l
Highest score = 87
2l + 7 = 87
(iv) 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).
Let the base angle be b in degrees
Base angles of isosceles triangle are congruent.
Vertex angle = 2b
Sum of the three angles of a triangle is 1800.
required equation is 2b + b + b = 180
4b = 180.
Click here for the solutions of
