2a + 2b = c subtract 2a from both sides 2a - 2a + 2b = c - 2a 2b = c - 2a divide both sides by 2 (2/2)b = (c - 2a)/2 b = (c - 2a)/2 --------------------
a-b+a-b+2b+a = 4a
2a + 2b = 160 But b = a + 40 so 2a + 2(a + 40) = 160 ie 2a + 2a + 80 = 160 or 4a = 80 ie a = 20 Then b = a + 40 gives b = 20 + 40 = 60 Solution: a = 20, b = 60
A = 2b + cSubtract 'c' from each side:A - c = 2bDivide each side by 2:b = 1/2 (A - c)
-2a plus 3b
2a + 2b = c subtract 2a from both sides 2a - 2a + 2b = c - 2a 2b = c - 2a divide both sides by 2 (2/2)b = (c - 2a)/2 b = (c - 2a)/2 --------------------
2a+2b+3a+3b+a+b= 6a+6b 2a+3a+a=6a 2b+3b+b=6b
(a - 2b)(2a - b)
a-b+a-b+2b+a = 4a
It is 2a-b simplified
6 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -36 is the average of 2a and a - 2b so 12 = 2a + a - 2b = 3a - 2b3 is the average of 2a - b and 4a + 3b so 6 = 2a - b + 4a + 3b = 6a + 2bAdding the two equations gives: 18 = 9a so that a = 2Substituting for a in the first gives 12 = 6 - 2b so that b = -3
2(a+b) is 2a plus 2b in factored form.
1
2a + 2b = 160 But b = a + 40 so 2a + 2(a + 40) = 160 ie 2a + 2a + 80 = 160 or 4a = 80 ie a = 20 Then b = a + 40 gives b = 20 + 40 = 60 Solution: a = 20, b = 60
Yes. For example, 7 - 3 = 4. You will always get an even number when adding or subtracting an odd and an odd. Let A & B be two odd numbers, so find out if A - B is even or odd. A = 2a +1 & B = 2b + 1 {little a & b are any integers, multiplying by 2 guarantees that 2a is even, then adding 1 will make it odd} A-B = 2a+1 - (2b+1) = 2a + 1 - 2b - 1 = 2a - 2b = 2(a-b). So (a-b) is some integer, but you multiply by 2, so the answer is even. Add A+B = 2a+1 + 2b+1 = 2a + 2b + 2 = 2(a+b+1), so again we are multiplying 2 by some integer, and get an even number.
4(2a+b) + 2(6a+2b) Working this out it is: 8a + 4b + 12a + 4b = 20a + 8b or 4(5a+2b).
= a + b - 2