What two expressions are equivalent to 14x – 10 – 6x? This question often arises in algebra, where simplifying expressions is a fundamental skill. To find the equivalent expressions, we need to combine like terms and understand the properties of algebraic operations. In this article, we will explore how to identify and simplify these expressions and provide a step-by-step solution.
In algebra, equivalent expressions are those that have the same value for all possible values of the variable. To determine if two expressions are equivalent, we can simplify both expressions and compare their simplified forms. In this case, we are given the expression 14x – 10 – 6x, and we need to find two equivalent expressions.
The first step in simplifying the given expression is to combine like terms. Like terms are terms that have the same variable and exponent. In our expression, 14x and -6x are like terms because they both have the variable x. To combine these like terms, we subtract the coefficients (the numbers in front of the variables):
14x – 6x = 8x
Now, we have simplified the expression to 8x – 10. To find two equivalent expressions, we can manipulate the original expression by adding or subtracting the same value from both sides of the equation. Let’s consider two examples:
1. Adding 4 to both sides of the equation:
14x – 10 – 6x + 4 = 8x – 10 + 4
8x – 6 = 8x – 6
The resulting expression, 8x – 6, is equivalent to the original expression, 14x – 10 – 6x.
2. Multiplying both sides of the equation by 2:
(14x – 10 – 6x) 2 = (8x – 10) 2
28x – 20 – 12x = 16x – 20
The resulting expression, 28x – 20 – 12x, is also equivalent to the original expression, 14x – 10 – 6x.
In conclusion, two expressions equivalent to 14x – 10 – 6x are 8x – 6 and 28x – 20 – 12x. By combining like terms and applying the properties of algebraic operations, we can identify and simplify equivalent expressions, which is a crucial skill in algebra.
