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 = x^{2}
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
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