## Chapter 6 – Simple Linear Equations ASSIGNMENT

POINTS TO REMEMBER

1. Equation: An equation is a statement which states that two expressions are equal.

2. To solve an equation means to find the value of the variable (unknown quantity) used in it.

Note: An equation remains unchanged if
(i) the same number is added to each side of the equation. .
(ii) the same number is subtracted from each side of the equation.
(iii) the same number is multiplied to each side of the equation.
(iv) Each side of the equation is divided by the same non-zero number.
(v) In transposing any term of an equation from one side to another, then its sign is reversed is
(a) from positive to negative and from negative to positive
(b) from multiplication to division and from division to multiplication.

3. In equation :
It is a statement of inequality between two expressions involving a single variable with the highest power one.

4. Replacement set
For a given inequation, the set from which the values of its variable are taken is called the replacement set or domain of the variable.

5. Solution set
It is the subset of the replacement set, consisting of those values of the variable which satisfy the given inequation

6. Properties of inequations
Adding, subtracting, multiplying or dividing by the same positive number to each side of an inequation does not change the inequality but multiplying or dividing by a negative number to each side of an inequation, it changes the inequality.

e.g.
Q1: Solve 2 + y=7

2 + y = 7
⇒ = 7- 2 = 5
Assignment

1) The sum of two consecutive even numbers is 38. Find the numbers.

2) A 300 m long wire is used to fence a rectangular plot whose length is twice its width. Find the length and breadth of the plot.

3) My mother is 12 years more than twice my age. After 8 years, my mother’s age will be 20 years less than three times my age. Find my age and my mother’s age.

4) In an isosceles triangle, the base angles are equal and the vertex angle is 80°. Find the measure of the base angles.

5) Seven times the number is 36 less than 10 times the number. Find the number.

6) Convert the following statements into equations :
(a) 5 added to a number is 9.
(b) 3 subtracted from a number is equal to 12.
(c) 5 times a number decreased by 2 is 4.
(d) 2 times the sum of the number x and 7 is 13.

7) Solve the following by trial and error method :
a) 2x-5 =3
b) 4m+7 = 3m+10

a) 6(k – 7) – 2 = 6
b) 2p – 6 = 8 + 5(p + 9)
c) 3(p + 8) = –6(p + 6)

9) Solve the following equations using the systematic method :
a) 3z+12 = 15
b) 8x = 20+3x

10) The father is 24 years older than his daughter. In 4 years, he will be thrice as old as his daughter. Find their present ages.

11 ) Five times a number exceeds 60 by 5. Find the number.

12) The ratio of two numbers is 2:5 and their difference is 63. What is the larger number?

1) 18 and 20
2) 50m and 100m
3) 16 yrs and 44 yrs
4) 50
5) 12
6) a) x+5 = 9 b) x-3 = 12
7) a) 4 b) 3
8) a) 25/3
9) a) 1
b) -59/3
b)4
10) 8 yrs and 32 yrs
11) 13
12) 105
c) 5x-2 = 4
c) -20/3
d) 2(x+7) = 13