NCERT Exercise 4.1 Solution
Simple Equations 7th Math
NCERT Exercise 4.1 Solution
What is an Equation?
An equation is a condition on variable. The condition is that two expressions should have equal value. Note that at least one of the two expressions must contain the variable.
In other words,
An equation has one or two expressions with equal sign.
Or, an equation has variables and constants with equal sign.
Some examples of equations:
(a) 2y = 4
(b) 2m + 4 = 10
(c) 12n + 5 = 4n +1
Characteristics of Equations
(a) An equation has mainly two parts. LHS (Left hand side) and RHS (Right hand side) with equal sign in the middle.
(b) An equation must has at least one variable.
(c) An equation must has an equal sign between LHS and RHS
(d) RHS or LHS of an equal may be only a number.
(e) An equation must have at least one of the two expressions with a variable.
(f) An equation remains the same, when the expression on the left and on the right are interchanged.
NCERT Exercise 4.1
Question (1) Complete the last column of the table
| S.No. | Equation | Value | Say, whether the equation is satisfied. (Yes/No) |
|---|---|---|---|
| (i) | x + 4 = 0 | x = 3 | |
| (ii) | x + 3 = 0 | x = 0 | |
| (iii) | x + 3 = 0 | x = – 3 | |
| (iv) | x – 7 = 1 | x = 7 | |
| (v) | x – 7 = 1 | x = 8 | |
| (vi) | 5x = 25 | x = 0 | |
| (vii) | 5x = 25 | x = 5 | |
| (viii) | 5x = 25 | x = – 5 | |
| (ix) | m/3 = 2 | m = – 6 | |
| (x) | m/3 = 2 | m = 0 | |
| (xi) | m/3 = 2 | m = 6 |
Answer
| S.No. | Equation | Value | Say, whether the equation is satisfied. (Yes/No) |
|---|---|---|---|
| (i) | x + 4 = 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 |
Explanations
(i) x + 3 = 0 when x = 3
Answer = No
Explanation
After substituting the value of x = 3 in the given equation, we have
3 + 3 = 0
⇒ 6 = 0
Thus, value of x = 3 for the given equation does not satisfy the equation.
Hence, Answer = No
(ii) x + 3 = 0 when x = 0
Answer = No
Explanation
After substituting the value x = 0 in the given equation, we get
0 + 3 = 0
⇒ 3 = 0
Thus, value of x = 0 for the given equation, does not satisfy the equation.
Thus, Answer = No
(iii) x + 3 = 0 when x = – 3
Solution
Given, x + 3 = 0 when x = – 3
After substituting the value of x = –3 in the given equation, we get
–3 + 3 = 0
⇒ 0 = 0
Thus, value of x = – 3 satisfies the given equation,
Thus, Answer = Yes
(iv) x – 7 = 1 when x = 7
Solution
Given, x – 7 = 1 when x = 7
After substituting the value x = 7 in the given equation, we get
7 – 7 =1
⇒ 0 = 1
Thus, value x = 7 does not satisfy the given equation, thus,
Answer = No
(v) x – 7 = 1 when x = 8
Solution
Given, x – 7 = 1 when x = 8
After substituting the value x = 8 in the given equation, we get
8 – 7 = 1
⇒ 1 = 1
Thus, value x = 8 satisfies the given equation,
Thus, Answer = Yes
(vi) 5 x = 25 when x = 0
Solution
Given, 5 x = 25 when x = 0
After substituting the value of x = 0 in the given equation, we get
5 × 0 = 25
⇒ 0 = 25
Thus, value of x = 0 does not satisfy the given equation,
Thus, Answer = No
(vii) 5 x = 25 when x = 5
Solution
Given, 5 x = 25 when x = 5
After substituting the value of x = 5 in the given equation, we get
5 × 5 = 25
⇒ 25 = 25
Thus, value of x = 5 satisfies the given equation,
Thus, Answer = Yes
(viii) 5 x = 25 when x = – 5
Solution
Given, 5 x = 25 when x = – 5
After substituting the value of x = – 5 in the given equation, we get
5 × (– 5) = 25
⇒ – 25 = 25
Since, value of x = – 5 does not satisfy the given equation,
Thus, Answer = No
(ix) m/3 = 2 when m = – 6
Solution
Given, m/3 = 2 when m = – 6
After substituting the value of m = - 6 in the given equation, we get
– 6/3 = 2
⇒ – 2 = 2
Since, value m = – 6 does not satisfy the given equation,
Thus, Answer = No
(x) m/3 = 2 when m = 0
Solution
Given, m/3 = 2 when m = 0
After substituting the value of m = 0 in the given equation, we get
0/3 = 2
⇒ 0 = 2
Since, the value m = 0 does not satisfy the given equation,
Thus, Answer = No
(xi) m/3 = 2 when m = 6
Solution :
Given, m/3 = 2 when m = 6
After substituting the value of m = 6 in the given equation, we get’
6/3 = 2
⇒ 2 = 2
Since, the value m = 6 satisfies the given equation,
Thus, Answer = Yes
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