Simplify the following
a) 4x-(3-x)
b) 9x-(8x+7y)
c) (a-3b)-(5a-8b)
a) 5x-3
b) x-7y
c) -4a+5b
a) To simplify 4x - (3 - x), we proceed according to the distributive property. When we distribute the negative sign inside the parentheses, it changes the signs of both terms inside. So we have:
4x - (3 - x) = 4x - 3 + x
Combining like terms, we get:
4x - (3 - x) = 5x - 3
Therefore, the simplified form of 4x - (3 - x) is 5x - 3.
b) To simplify 9x - (8x + 7y), we again apply the distributive property. When we distribute the negative sign, it changes the signs of both terms inside the parentheses:
9x - (8x + 7y) = 9x - 8x - 7y
Combining like terms, we get:
9x - (8x + 7y) = x - 7y
Thus, the simplified form of 9x - (8x + 7y) is x - 7y.
c) To simplify (a - 3b) - (5a - 8b), we apply the distributive property twice. When we remove the parentheses, we need to change the signs of all terms inside the second set of parentheses:
(a - 3b) - (5a - 8b) = a - 3b - 5a + 8b
Now, we combine like terms:
(a - 3b) - (5a - 8b) = (-5a + a) + (-3b + 8b)
Simplifying further, we have:
(a - 3b) - (5a - 8b) = -4a + 5b
Thus, the simplified form of (a - 3b) - (5a - 8b) is -4a + 5b.