Simple Equations

Exercise 4.1

Question 1: Complete the last column of the table.

S. No.EquationValueEquation 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:

  1. `n + 5 = 19 (n = 1)`

    Answer: `n + 5 = 19`
    Or, `n = 19 – 5 = 14`
    Hence, the value in the bracket is not correct.
  2. `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.
  3. `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.
  4. `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.
  5. `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.
  6. `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:

  1. `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.
  2. `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:

  1. The sum of numbers x and 4 is 9.

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

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

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

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

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

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

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

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

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

  10. Question 5: Write the following equations in statement forms:

    1. `p + 4 = 15`

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

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

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

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

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

      Answer: When 4 is added to three times of p, we get 25.
    7. `4p – 2 = 18`

      Answer: When 2 is subtracted from 4 times p, we get 18.
    8. `(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:

    1. 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`
    2. 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`
    3. 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`
    4. 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°`


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