Chapter 4 Simple Equations Exercise 4.1
Question 1: Complete the last column of the table.
S. No. |
Equation |
Value |
Say, whether the equation is satisfied. (Yes/No) |
1 |
x + 3 = 0 |
x = 3 |
= 3 + 3 ≠ 0 Therefore, the equation is not satisfied. |
2 |
x + 3 = 0 |
x = 0 |
= 0 + 3 ≠ 0 Therefore, the equation is not satisfied. |
3 |
x + 3 = 0 |
x = -3 |
= -3 + 3 = 0 Therefore, the equation is satisfied. |
4 |
x – 7 = 1 |
x = 7 |
= 7 - 7 ≠ 1 Therefore, the equation is not satisfied. |
5 |
x – 7 = 1 |
x = 8 |
= 8 - 7 = 1 Therefore, the equation is satisfied. |
6 |
5x = 25 |
x = 0 |
= 5 x 0 ≠ 25 Therefore, the equation is not satisfied. |
7 |
5x = 25 |
x = 5 |
= 5 x 5 = 25 Therefore, the equation is satisfied. |
8 |
5x = 25 |
x = -5 |
= 5 x -5 ≠ 25 Therefore, the equation is not satisfied. |
9 |
(m/3) = 2 |
m = – 6 |
= -6/2 ≠ 2 Therefore, the equation is not satisfied. |
10 |
(m/3) = 2 |
m = 0 |
= 0/3 ≠ 2 Therefore, the equation is not satisfied. |
11 |
(m/3) = 2 |
m = 6 |
= 6/2 = 3 Therefore, the equation is satisfied. |
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:
LHS |
RHS |
1 + 5 |
19 |
6 |
19 |
6 ≠ 19
Therefore, the value n = 1 is not a solution to n + 5 = 19.
(b) 7n + 5 = 19 (n = – 2)
Answer:
LHS |
RHS |
7
x (-2) + 5 |
19 |
-9 |
19 |
-9 ≠ 19
Therefore, the value n = -2 is not a solution to 7n + 5 = 19.
(c) 7n + 5 = 19 (n = 2)
Answer:
LHS |
RHS |
7
x 2 + 5 |
19 |
9 |
19 |
9 = 19
Therefore, the value n = 2 is a solution to 7n + 5 = 19.
(d) 4p – 3 = 13 (p = 1)
Answer:
LHS |
RHS |
4 x 1 - 3 |
13 |
1 |
13 |
1 ≠ 13
Therefore, the value p = 1 is not a solution to 4p – 3 = 13.
(e) 4p – 3 = 13 (p = – 4)
Answer:
LHS |
RHS |
4 x (-4) - 3 |
13 |
= -16 - 3 |
13 |
-19 ≠ 13
Therefore, the value p = -4 is not a solution to 4p – 3 = 13.
(f) 4p – 3 = 13 (p = 0)
Answer:
LHS |
RHS |
4 x 0 - 3 |
13 |
= 0 - 3 |
13 |
-3 ≠ 13
Therefore, the value p = 0 is not a solution to 4p – 3 = 13.
Question 3: Solve the following
equations by trial and error method:
(i) 5p + 2 = 17
Answer:
p |
5p +2 |
= 17 |
0 |
=
5 x 0 + 2 |
No |
1 |
=
5 x 1 + 2 |
No |
2 |
=
5 x 2 + 2 |
No |
3 |
=
5 x 3 + 2 |
Yes |
(ii) 3m – 14 = 4
Answer:
m |
3m - 14 |
= 4 |
0 |
=
3 x 0 - 14 |
No |
1 |
=
3 x 1 - 14 |
No |
2 |
=
3 x 2 - 14 |
No |
3 |
=
3 x 3 - 14 |
No |
4 |
=
3 x 4 - 14 |
No |
5 |
=
3 x 5 - 14 |
No |
6 |
=
3 x 6 - 14 |
Yes |
Question 4: Write equations for the
following statements:
(i) The sum of numbers x and 4 is 9.
Answer: x + 4 = 9
(ii) 2 subtracted from y is 8.
Answer: y - 2 = 8
(iii) Ten times a is 70.
Answer: 10a = 70
(iv) The number b divided by 5 gives
6.
Answer: b/5 = 6
(v) Three-fourth of t is 15.
Answer: 3/4 t =
15
(vi) Seven times m plus 7 gets you
77.
Answer: 7m + 7
= 77
(vii) One-fourth of a number x minus
4 gives 4.
Answer: 1/4 x - 4
= 4
(viii) If you take away 6 from 6
times y, you get 60.
Answer: 6y - 6 =
60
(ix) If you add 3 to one-third of z,
you get 30.
Answer: 1/3 z + 3
= 30
Question 5: Write the following
equations in statement forms:
(i) p + 4 = 15
Answer: The sum
of numbers p and 4 is 15.
(ii) m – 7 = 3
Answer: 7
subtracted from m is 3.
(iii) 2m = 7
Answer: Twice of
number m is 7.
(iv) m/5 = 3
Answer: The
number m divided by 5 gives 3.
(v) (3m)/5 = 6
Answer:
Three-fifth of m is 6.
(vi) 3p + 4 = 25
Answer: Three
times p plus 4 gives you 25.
(vii) 4p – 2 = 18
Answer: Four
times p minus 2 gives you 18.
(viii) p/2 + 2 = 8
Answer: If you
add half of a number p to 2, you get 8.
Question 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.)
Answer:
Number of marbles Parmit has = m
Irfan has 7 marbles more than five times the marbles Parmit has
= 5 x number of Parmit’s marbles + 7 = Total number of marbles Irfan having
= (5 x m) + 7 = 37
= 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.)
Answer:
Let Laxmi’s age be = y years old
Laxmi’s father is 4 years older than three times of her age
= 3 x Laxmi’s age + 4 = Age of Laxmi’s father
= (3 x y) + 4 = 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.)
Answer:
Highest score in the class = 87
Let the lowest score be l.
= 2 x lowest score + 7 = highest marks in the class
= (2 x l) + 7 = 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).
Answer:
Let the base angle be b.
Vertex angle = 2 x base angle = 2b
= b + b + 2b = 180°
= 4b = 180°
No comments:
Post a Comment