Answer:
Option A
Step-by-step explanation:
Given:
- a. 3x-5= 3x + 5
- b. 3x-5= 3x - 5
- c. 3x - 5 = 2x+5
- d. 3x-5 = 2x + 10
To find:
- Which one of the linear equations have no solution.
Solution:
a) 3x-5= 3x + 5
Add 5 to both sides
3x-5= 3x + 5
3x - 5 + 5 = 3x + 5 + 5
Simplify
(Add the numbers)
3x - 5 + 5 = 3x + 5 + 5
3x = 3x + 5 + 5
(Add the numbers)
3x = 3x + 5 + 5
3x = 3x + 10
Subtract 3x from both sides
3x = 3x + 10
3x - 3x = 3x + 10 - 3
Simplify
(Combine like terms)
3x -3x = 3x + 10 - 3
0 = 3x + 10 - 3
(Combine like terms)
0 = 3x + 10 - 3
0 = 10
The input is a contradiction: it has no solutions
b) 3x-5= 3x - 5
Since both sides equal, there are infinitely many solutions.
c) 3x - 5 = 2x+5
Add 5 to both sides
3x = 2x + 5 + 5
Simplify 2x + 5 + 5 to 2x + 10
3x = 2x + 10
Subtract 2x from both sides
3x - 2x = 10
Simplify 3x - 2x to x.
x = 10
d) 3x-5 = 2x + 10
Add 5 to both sides
3x = 2x + 10 + 5
Simplify 2x + 10 + 5 to 2x + 15
3x = 2x + 15
Subtract 2x from both sides
3x - 2x = 15
Simplify 3x -2x to x.
x = 15
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Answer:
As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.
Therefore, <u><em>Option A</em></u> is the linear equation that has no solution.
Answer:
-3 <x <-1
Step-by-step explanation:
|x + 2| < 1
There are two solutions, one positive and one negative ( remember to flip the inequality for the negative)
x+2 <1 and x+2 > -1
Subtract 2 from each side
x+2-2 < 1-2 and x+2-2 > -1-2
x < -1 and x >-3
-3 <x <-1
The half-life is 29 years.
116 : 29 = 4
So we will have 4 periods of half-life:
( 1/2 )^4 = 1/16
150 g * 1/16 = 9.375 g
Answer:
9.375 g of strontium -90 will remain after 116 years.
Answer:
12 percent
Step-by-step explanation:
The tip is 24.64 - 22 = 2.64
2.64 / 22 = 0.12
Answer:
x - 1
Step-by-step explanation:
x
x - 1
x - 2
x + (x - 1) + ( x - 2)
3x - 3
3(x - 1)
Average
3(x - 1)/3
x - 1