Hello!
We can go through each equation to solve:
1.
x + 3 = 4(x - 1) + 2
Distribute the coefficient outside of the parenthesis:
x + 3 = 4(x) + 4(-1) + 2
Simplify:
x + 3 = 4x - 4 + 2
x + 3 = 4x - 2
Subtract x from both sides:
3 = 3x - 2
Add 2 to both sides:
5 = 3x
Divide both sides by 3:
5/3 = x. This is not the answer.
2.
2x - 8 = 7 - 3x
Add 3x to both sides:
5x - 8 = 7
Add 8 to both sides:
5x = 15
Divide both sides by 5:
5x/5 = 15/5
x = 3. This is an answer.
3.
3(x + 2) = 14 - x
Distribute:
3(x) + 3(2) = 14 - x
3x + 6 = 14 - x
Add x to both sides:
4x + 6 = 14
Subtract 6 from both sides:
4x = 8
Divide both sides by 4:
4x/4 = 8/4
x = 2. This is not an answer.
4.
4(x - 1) = x + 5
Distribute:
4x - 4 = x + 5
Subtract x from both sides:
3x - 4 = 5
Add 4 to both sides:
3x = 9
Divide both sides by 3:
3x/3 = 9/3
x = 3. This is an answer.
5.
5 - 2(x + 1) = x
Distribute:
5 - 2x - 2 = x
Simplify:
3 - 2x = x
Add 2x to both sides:
3 = 3x
Divide both sides by 3:
3/3 = 3x/3
x = 1. This is not an answer.
6.
6(x - 4) = 2x
Distribute:
6x - 24 = 2x
Subtract 6x from both sides:
-24 = -4x
Divide both sides by -4:
-24/(-4) = -4x/(-4)
x = 6. This is not an answer.
Total amount earned after 16 years = $93649
Explanation:The principal, P = $50,000
Interest rate, r = 4% = 4/100
r = 0.04
The time, t = 16 years
Number of times intesrest is compounded per year, n = 1
Total amount is calculated below:
Total amount earned after 16 years = $93649
Answer:
Answer:
(a)There are 500 integers from 1 through 1,000 are multiples of 2.
There are 111 integers from 1 through 1,000 are multiples of 9.
(b)0.611
Step-by-step explanation:
Given the set of Integers from 1 through 1000
The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,
where first term, a =2, common difference, d =2
Nth term of an A.P,
Similarly,
Given the set of Integers from 1 through 1000
The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,
where first term, a =9, common difference, d =9
Nth term of an A.P,
(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.
There are a total of 1000 numbers between from 1 through 1,000
n(S)=1000
n(Multiples of 2)=500
n(Multiples of 9)=111
Therefore: