Class 7 Maths

Simple Equations

Exercise 4.1

Question 1: Complete the last column of the table.

S. No.EquationValueSay whether the equation 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:

  • `n + 5 = 19 (n = 1)`

    Answer: `n + 5 = 19`
    Or, `n = 19 – 5 = 14`
    Hence, the value in the bracket is not correct.
  • `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.
  • `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.
  • `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.
  • `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.
  • `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:

  • `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.
  • `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:

  • The sum of numbers x and 4 is 9.

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

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

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

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

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

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

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

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

    Answer: `(z/3) + 3 = 30`

Question 5: Write the following equations in statement forms:

  • `p + 4 = 15`

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

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

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

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

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

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

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

  • 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`
  • 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`
  • 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`
  • 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°`