Answer:
The number is 15.
Step-by-step explanation:
Finding the Value of a Number Using the Algebraic Equation
To find the value of a number, we need to translate the mathematical phrases to algebraic equation.
What is algebraic equation?
Algebraic equation is the statement of the equality of two algebraic expressions.
What is algebraic expression?
An algebraic expression is a combination of constant, variables and algebraic operations.
Constant
Constant is the known value in an equation and does not change its value.
Variable
It is a symbol or letter, such as "x" or "y," that represents an unknown value.
Operation
These are the four basic operations: addition, subtraction, multiplication and division.
Equation:
Translating Phrases to Algebraic Expressions
Let x be the number.
THRICE A NUMBER, DECREASED BY 4 = 3x - 4
TWICE THE NUMBER, INCREASED BY 11 = 2x + 11
Algebraic Equation
"thrice a number, decreased by 4 IS THE SAME AS twice the number, increased by 11"
The highlighted phrase means that the expressions are equal.
3x - 4 = 2x + 11
Solution:
Combine similar terms.
3x - 4 = 2x + 11
3x - 2x = 11 + 4
x = 15
Final Answer:
The number is 15.
Checking:
3x - 4 = 2x + 11
3(15) - 4 = 2(15) + 11
45 - 4 = 30 + 11
41 = 41 ✔
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