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:

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

Answer: `n + 5 = 19`

Or, `n = 19 – 5 = 14`

Hence, the value in the bracket is not correct.

(b) `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.

(c) `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.

(d) `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.

(e) `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.

(f) `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:

(a) `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.

(b) `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:

(a) The sum of numbers x and 4 is 9.

Answer: `x + 4 = 9`

(b) 2 subtracted from y is 8.

Answer: `y – 2 = 8`

(c) Ten times a is 70.

Answer: `10a = 70`

(d) The number b divided by 5 gives 6.

Answer: `b/5 = 6`

(e) Three-fourth of t is 15.

Answer: `(3/4)t = 15`

(f) Seven times m plus 7 gets you 77.

Answer: `7m +7 = 77`

(g) One-fourth of a number x minus 4 gives 4.

Answer: `(x/4) – 4 = 4`

(h) If you take away 6 from 6 times y, you get 60.

Answer: `6y – 6 = 60`

(i) 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:

(a) `p + 4 = 15`

Answer: Sum of p and 4 is 15.

(b) `m – 7 = 3`

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

(c) `2m = 7`

Answer: Two times m is 7.

(d) `m/5 = 3`

Answer: One fifth of m is 3.

(e) `(3m)/(5) = 6`

Answer: Three fifth of m is 6.

(f) `3p + 4 = 25`

Answer: When 4 is added to three times of p, we get 25.

(g) `4p – 2 = 18`

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

(h) `(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:

(a) 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`

(b) 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`

(c) 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`

(d) 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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