# Simple Equations

## Exercise 4.1

**Question 1:** Complete the last column of the table.

S. No. | Equation | Value | Equation is satisfied (Yes/No) |
---|---|---|---|

(a) | x + 3 = 0 | x = 3 | |

(b) | x + 3 = 0 | x = 0 | |

(c) | x + 3 = 0 | x = -3 | |

(d) | x – 7 = 1 | x = 7 | |

(e) | x – 7 = 1 | x = 8 | |

(f) | 5x = 25 | x = 5 | |

(g) | 5x = 25 | x = -5 | |

(h) | m/3 = 2 | m = - 6 | |

(i) | m/3 = 2 | m = 0 | |

(j) | m/3 = 2 | m = 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°`