Beth got a job painting dorm rooms at her college. At top speed, she could paint 5 identical rooms during one 6-hour shift. How
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Simplify both sides if needed. The left-hand side needs simplification.
4(x - 6)
-2x + 6
4x - 24 -2x + 6
All is left to do is add and subtract to get the x variable all alone.
4x - 24 -2x + 6
6x - 24 6 <-- Add 2x to both sides
6x 30 <-- Add 24 to both sides
x 5 <-- Divide both sides by 6
In order to be in the solution set, x has to be less than or equal to 5.
In interval notation: [5, -∞)
4(x - 6)
4x - 24
All is left to do is add and subtract to get the x variable all alone.
4x - 24
6x - 24
6x
x
In order to be in the solution set, x has to be less than or equal to 5.
In interval notation: [5, -∞)
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct