Answer:
The number is 5
Step-by-step explanation:
Solution:
Given that a number increased by 6 is equal to 11, let x represent that number. Then, x + 6 = 11.
To solve for x, add the additive inverse of 6 to both sides of the equation such that, x + 6 + (-6) = 11 + (-6).
Simplifying it will give: x + 6 - 6 = 11 - 6. Therefore, x = 5.
To check, replace x with 5 such that x + 6 = 11. Then, 5 + 6 = 11. Thus, 11 = 11.
Other Examples:
There are b boys in the class. This is three more than four times the number of girls. How many girls are in the class?
To solve this problem, use the following representations:
b - number of boys
g - number of girls
Therefore, b = 4g + 3
2. The sum of two numbers is 84, and one of them is 12 more than the
other. What are the two numbers?
x - be the first number
Given that one of the two numbers is 12 more than the other then,
x + 12 = second number
Then, x + (x + 12) = 84
2x + 12 = 84
Add the additive inverse of 12 to both sides of the equation such that,
2x + 12 + (-12) = 84 + (-12)
2x = 84 - 12
2x = 72
Divide both sides of the equation by 2 to solve for x.
2x/2 = 72/2
x = 36
Therefore, the first number is 36. Solve for the other number.
x + 12 = 36 + 12 = 48
The second number is 48.
To check, x + (x + 12) = 84. Then, 36 + 48 = 84.
Keywords: number, algebraic expression
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Answers & Comments
Answer:
The number is 5
Step-by-step explanation:
Solution:
Given that a number increased by 6 is equal to 11, let x represent that number. Then, x + 6 = 11.
To solve for x, add the additive inverse of 6 to both sides of the equation such that, x + 6 + (-6) = 11 + (-6).
Simplifying it will give: x + 6 - 6 = 11 - 6. Therefore, x = 5.
To check, replace x with 5 such that x + 6 = 11. Then, 5 + 6 = 11. Thus, 11 = 11.
Other Examples:
There are b boys in the class. This is three more than four times the number of girls. How many girls are in the class?
To solve this problem, use the following representations:
b - number of boys
g - number of girls
Therefore, b = 4g + 3
2. The sum of two numbers is 84, and one of them is 12 more than the
other. What are the two numbers?
To solve this problem, use the following representations:
x - be the first number
Given that one of the two numbers is 12 more than the other then,
x + 12 = second number
Then, x + (x + 12) = 84
2x + 12 = 84
Add the additive inverse of 12 to both sides of the equation such that,
2x + 12 + (-12) = 84 + (-12)
2x = 84 - 12
2x = 72
Divide both sides of the equation by 2 to solve for x.
2x/2 = 72/2
x = 36
Therefore, the first number is 36. Solve for the other number.
x + 12 = 36 + 12 = 48
The second number is 48.
To check, x + (x + 12) = 84. Then, 36 + 48 = 84.
Keywords: number, algebraic expression