A variable is something that changes and have different numbers. We use letters like a, b, or c to stand for these variables. We can make expressions by doing math with these variables—like adding, subtracting, multiplying, or dividing. For example, if we have a variable called a, we can make the equation (3a + 6) by multiplying a by 3 and then adding 6.
The expression’s value changes depending on the number of the variable. If a is 2, then 3a + 6 becomes 3 times 2 plus 6, which equals 12. If a is 10, the equation (3a + 6) turns into 3 times 10 plus 6, which is 36.
If we have the equation 3a + 6 = 36, 3a + 6 must equal 36. To make this true, a should be 10, because 3 times 10 plus 6 is 36. If a is not 10, like if it’s 2, then 3 times 2 plus 6 is 12, not 36. So, if a is 2 then it is not the right answer to this equation. In the exercise 4.1 Simple Equations, we would solve questions based on these concepts.
NCERT Solutions for Class 7 Maths Exercise 4.1 Chapter 4 Simple Equations
1. Complete the last column of the table.
| 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 |
2. Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1)
Substitute n = 1:
1 + 5 = 6
6 is not equal to 19.
So, n = 1 is not a solution.
(b) 7n + 5 = 19 (n = –2)
Substitute n = –2:
7(-2) + 5 = -14 + 5 = -9
-9 is not equal to 19.
So, n = –2 is not a solution.
(c) 7n + 5 = 19 (n = 2)
Substitute n = 2:
7(2) + 5 = 14 + 5 = 19
19 is equal to 19.
So, n = 2 is a solution.
(d) 4p – 3 = 13 (p = 1)
Substitute p = 1:
4(1) – 3 = 4 – 3 = 1
1 is not equal to 13.
So, p = 1 is not a solution.
(e) 4p – 3 = 13 (p = –4)
Substitute p = –4:
4(-4) – 3 = -16 – 3 = -19
-19 is not equal to 13.
So, p = –4 is not a solution.
(f) 4p – 3 = 13 (p = 0)
Substitute p = 0:
4(0) – 3 = 0 – 3 = -3
-3 is not equal to 13.
So, p = 0 is not a solution.
3. Solve the following equations by trial and error method:
(i) 5p + 2 = 17
Trying p = 3:
5(3) + 2 = 15 + 2 = 17
17 equals 17.
Solution: p = 3.
(ii) 3m – 14 = 4
Trying m = 6:
3(6) – 14 = 18 – 14 = 4
4 equals 4.
Solution: m = 6.
4. Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
Equation: x + 4 = 9
(ii) 2 subtracted from y is 8.
Equation: y – 2 = 8
(iii) Ten times a is 70.
Equation: 10a = 70
(iv) The number b divided by 5 gives 6.
Equation: b / 5 = 6
(v) Three-fourth of t is 15.
Equation: (3/4)t = 15
(vi) Seven times m plus 7 gets you 77.
Equation: 7m + 7 = 77
(vii) One-fourth of a number x minus 4 gives 4.
Equation: (1/4)x – 4 = 4
(viii) If you take away 6 from 6 times y, you get 60.
Equation: 6y – 6 = 60
(ix) If you add 3 to one-third of z, you get 30.
Equation: (1/3)z + 3 = 30
5. Write the following equations in statement forms:
(i) p + 4 = 15
Statement: The sum of number p and 4 equals 15.
(ii) m – 7 = 3
Statement: When 7 is subtracted from m, the result is 3.
(iii) 2m = 7
Statement: Twice the number m equals 7.
(iv) m/5 = 3
Statement: One fifth of m equals 3.
(v) 3m/5 = 6
Statement: Three fifths of m equals 6.
(vi) 3p + 4 = 25
Statement: Three times p plus 4 equals 25.
(vii) 4p – 2 = 18
Statement: Four times p minus 2 equals 18.
(viii) p/2 + 2 = 8
Statement: Half of p plus 2 equals 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.)
Irfan has 37 marbles, which is 7 more than five times the marbles Parmit has.
Equation: 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.)
Laxmi’s father is 49 years old, which is 4 years older than three times Laxmi’s age.
Equation: 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.)
The highest marks in a class are twice the lowest marks plus 7, with the highest score being 87.
Equation: 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).
In an isosceles triangle, the vertex angle is twice any base angle. The sum of all angles in a triangle is 180 degrees.
Equation: b + b + 2b = 180
Additional Worksheet Questions for Exercise 4.1 Simple Equations
1. Write the equations for the following statements:
(i) The sum of a number x and 6 is 10.
(ii) Twice a number y subtracted from 15 equals 3.
2. Solve for the variable:
(i) 7p – 5 = 16
(ii) 3m/4 = 9
3. If a number n is doubled and then increased by 4, the result is 18. Write the equation.
4. A rectangle’s length is three times its width w. If the perimeter is 48 cm, write the equation for the perimeter.
5. The ages of two siblings are in the ratio 3:4. If the younger sibling is 9 years old, write the equation to find the elder sibling’s age.
6. Create an equation: The product of 8 and a number k minus 5 is equal to 27.
7. An equation for a situation where a number t divided by 5 and then decreased by 2 equals 3.
8. If one-third of a number s is added to 7, the result is 13. Form the equation.
9. Write an equation: A number v decreased by 12 and then doubled gives 10.
10. An equation for the sum of three consecutive numbers n, n+1, n+2 being 36.
Answers
- (i) Equation: x + 6 = 10 (ii) Equation: 15 – 2y = 3
- (i) Solve: 7p = 21, p = 3 (ii) Solve: 3m = 36, m = 12
- Equation: 2n + 4 = 18
- Equation for perimeter: 2(3w) + 2w = 48
- Equation for elder sibling’s age: 4/3 * 9 = Elder’s age
- Equation: 8k – 5 = 27
- Equation: t/5 – 2 = 3
- Equation: s/3 + 7 = 13
- Equation: 2(v – 12) = 10
- Equation: n + (n+1) + (n+2) = 36
