Identify the property that justifies the statement: If 4x-3=7, then 4x=10
The Correct Answer and Explanation is:
Correct Answer: Addition Property of Equality
Explanation:
The Addition Property of Equality states that if you add the same number to both sides of an equation, the equality is still true. This property is used when you want to isolate a variable or simplify an equation in order to solve it.
Let us analyze the given statement:
We start with the equation:
4x − 3 = 7
To isolate the term with the variable (4x), you need to eliminate the constant −3 from the left-hand side. The inverse of subtraction is addition, so you add 3 to both sides of the equation:
(4x − 3) + 3 = 7 + 3
Simplifying both sides:
4x = 10
This step is justified by the Addition Property of Equality because we are adding the same number (3) to both sides of the equation to maintain balance. Using this property ensures the equation remains true as we transform it into a simpler form.
Here is why the property is important in solving equations:
- Maintains balance – Equations are like balanced scales. If you change one side, you must do the same to the other side.
- Moves constants – This property helps shift constants from one side to the other so that you can isolate the variable.
- Step-by-step solving – Algebraic equations are solved in steps. The addition property is often used early in the process to remove or cancel numbers from one side of the equation.
In conclusion, the transition from 4x − 3 = 7 to 4x = 10 uses the Addition Property of Equality, because you are adding 3 to both sides of the equation to eliminate the −3 and solve for x more easily.
