LINEAR EQUATIONS

1. Declare each of the following sentences as “true” of “false”!

a. 12 + 23 = 23 + 12 is the associative property of addition.

b. The product of 6 and 7 equals the product of 7 and 6.

c. The sum of two odd numbers is always an even number.

d. Year 2004 is a leap year.

e. 1 kg of foam rubber is lighter compared to 1 kg of iron.

f. 1 hour = 360 seconds.

g. The meaning of 6 ´ 4 is 6 + 6 + 6 +6.

h. a ´ (b + c) = (a ´ b) + (a ´ c) is the associative property.

i. The meaning of 34 is 3 ´ 3 ´ 3 ´ 3.

2. Copy and complete the following table!

Open sentence	True sentence	False sentence
∆ + 5 = 19  - 6 = 11 a ´ a = 169 q is a factor of 12	14 + 5 = 19 ……………. ……………. …………….	13 + 5 = 19 ……………. ……………. …………….

3. Find the substitutes for the variable so that sentence become true!

a. There are x weeks in one year .

b. y is the odd multiple of 3 which is less than 30.

c. z is a number between 20 and 35 which is divided out by 3.

d. p is a factor of 16

e. q ´ 4 = 12, z is an integer.

f. a is an even prime number.

4. Find the substitute for each variable so that the following sentences become true!

a. x + 9 = 17

b. y : 15 = 0

c. 6 ´ 9 = 18

d. p + p = 16

e. a – a = a

f. b : b = b

5. Find the substitute for each variable so that the following sentences become true!

a. k is a square number which is less than 20.

b. y is integer which is less than 40 and is evenly divided by 3 and 6

6. For question a to d, find their solutions!

a. One week consists of x days

b. A cube is formed by x congruent squares.

c. In one year there are x months each of which lasts for 31 days.

d. The number 30 has x prime factors.

7. Find the solutions of each of the following in open sentences !

a. x is a variable which takes on the numbers 1, 2, 4, 6, 8 and 10.

b. (x + 6) is less than 15

c. 3^x = 9

d. 2 ´ x = x²

e. x + 3 = 11 – x

8. If the variables take on natural numbers, find the solution of each of the following equations by substitution!

a. a + 4 = 9

b. n – 4 = 8

c. 8 = 10 – p

d. 4 – y = - 2

e. b +

f.

g. z ´ z = 49

h. y

9. If the variables take on rational numbers, find the solution of each of the following equations by substitutions!

a. 2y + y = 9

b. 45 : z = -5

c. 3p + 9 = 3

d. x – 2 = 6 – x

e. 4x

f. 8 – 2p =

g.

h. 4p – 2 = 2p + 8

10. Find the following or the solutions of each of the following equations. Work them out by adding to or subtracting from both sides of the equations the same quantity!

a. x + 4 = 7

b. x – 5 = 12

c. x – 9 = 6

d. y – 27 = - 18

e. 3y = 2y

f. 5y = 4y + 10