गिव मी द आंसर प्लीज प्लीज प्लीजSolve the following:
a) 8x – 3 = 6x
b) 9x = 15(7-6x)
c) 3(7y+4)= -4(y+3)
d) 9z = 4(z+15)
e) 6(4x+8)= 5(5x+8)
Answers
Associative Property
Rational numbers follow the associative property for addition and multiplication.
Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+z
For multiplication: x(yz)=(xy)z.
Example: 1/2 + (1/4 + 2/3) = (1/2 + 1/4) + 2/3
⇒ 17/12 = 17/12
And in case of multiplication;
1/2 x (1/4 x 2/3) = (1/2 x 1/4) x 2/3
⇒ 2/24 = 2/24
⇒1/12 = 1/12
Distributive Property
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
Example: 1/2 x (1/2 + 1/4) = (1/2 x 1/2) + (1/2 x 1/4)
LHS = 1/2 x (1/2 + 1/4) = 3/8
RHS = (1/2 x 1/2) + (1/2 x 1/4) = 3/8
Hence, proved
Identity and Inverse Properties of Rational Numbers
Identity Property: 0 is an additive identity and 1 is a multiplicative identity for rational numbers.
Examples:
1/2 + 0 = 1/2 [Additive Identity]
1/2 x 1 = 1/2 [Multiplicative Identity]
Inverse Property: For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.
Examples:
The additive inverse of 1/3 is -1/3. Hence, 1/3 + (-1/3) = 0
The multiplicative inverse of 1/3 is 3. Hence, 1/3 x 3 = 1