Question 340854: The sum of two numbers is greater than or equal to 14 . The second number is 2 less than the first. What are the possible values for the first of the two numbers?
In your answer, denote the first number by x.
The sum of two numbers is less than or equal to28 . The second number is 8 more than the first. What are the possible values for the first of the two numbers?
In your answer, denote the first number by x
Thank whoever help me I need these two answers badly. Thank you again!
Found 2 solutions by mananth, Theo:
Answer by mananth(16946)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! first problem:
x + y >= 14
y = x - 2
Substitute x-2 for y in the first equation to get:
x + x - 2 >= 14
Solve for x to get:
x >= 8
You do this by adding 2 to both sides of the equation and then combining terms on each side of the equation and then dividing both sides of the equation by 2.
Since y = x - 2, then y will always be 2 less than whatever x is.
Confirm by substituting for x and y in the original equation.
If x is greater than or equal to 8, the equation should be true, and if x is smaller than 8, the equation should be false.
Examples:
When x = 8, then y = 6, and x + y >= 14 becomes 14 >= 14 which is true.
When x = 6, then y = 4, and x + y >= 14 becomes 10 >= 14 which is false.
When x = 10, then y = 8, and x + y >= 14 becomes 18 >= 14 which is true.
second problem:
x + y <= 28
y = x + 8
Substitute x + 8 for y in the first equation to get:
x + x + 8 <= 28
Solve for x to get:
x <= 10
You do this by subtracting 8 from both sides of the equation and then combining like terms and then dividing both sides of the equation by 2.
Since y = x + 8, then y will always be 8 more than whatever x is.
Confirm by substituting for x and y in the original equation.
If x is smaller than or equal to 10, then the equation should be true.
If x is greater than 10, then he equation should be false.
Example:
When x = 10, y = 18, and x + y <= 28 becomes 28 <= 28 which is true.
When x = 12, y = 20, and x + y <= 28 becomes 32 <= 28 which is false.
When x = 8, y = 16, and x + y <= 28 becomes 24 <= 28 which is true.
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