Answer:
2x - 0.4x ;
8x/5 ;
Yes
Step-by-step explanation:
Let number of miles = x
Arlene:
Double number of miles = 2 * x = 2x
Subtract 20% of the result :
2x - 20% of 2x ;
2x - 0.4x
Raul:
Divides Number of miles by 5 ; x / 5
Multiplies result by 8 ;
8 * (x/5) = 8x /5
To know if expressions are equivalent :
Let x = 10 miles
Using Arlene's expression:
2x - 0.4x
x = 10
2(10) - 0.4(10) = 16
Using Raul's expression :
8x / 5
(8*10) / 5
80/5
= 16
Since they give the same result, we can conclude that the expression are equivalent
We have to simplify and get the value of x from this inequality given:
Given inequality,

Now let's simplify by using distributive property,

We need to find x, so let's isolate x to the letter side of the inequality for calculation at ease.


Now, dividing -2 from both sides.
Note : As we are dividing a negative number from both sides, the sign of the inequality will be <u>reversed</u>.


Now subtracting -7 from both sides,


Or, Interval of the equal ![(- \infin, -7 ]](https://tex.z-dn.net/?f=%28-%20%5Cinfin%2C%20-7%20%5D)
#CarryOnLearning
<u>━━━━━━━━━━━━━━━━━━━━</u>
Percent means parts out of 100
28%=28/100=14/50=7/25
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