Subtraction of Equality

Subtracting equality involves finding the difference between equal quantities by introducing the concept of maintaining balance. It requires ensuring that both sides of an equation remain equal after the subtraction.

There are three components of an expression in subtraction of equality:

Coefficients: These are constant values like -1, 4, etc.

Variables: These are unknown quantities like x, y, z, etc.

Operators: For subtraction, the operator is the minus (-) symbol.

When subtracting to maintain equality, students should follow these rules:

Maintain balance: Subtract the same value from both sides of the equation to keep it balanced.

Combine like terms: Only like terms can be subtracted from one another, so group all like terms together on each side of the equation.

Simplifying result: After all like terms are combined, simplify the equation to see if further operations are necessary to solve for variables.

The following methods are used for subtraction while maintaining equality:

Method 1: Horizontal Method

To apply the horizontal method for subtraction while maintaining equality, use these steps.

Step 1: Write the equation with the expressions on both sides.

Step 2: Subtract the same value from both sides.

Step 3: Combine like terms on each side. Let's apply these steps to an example:

Question: Subtract 3 from both sides of the equation x + 5 = 10.

Step 1: Write the equation x + 5 = 10.

Step 2: Subtract 3 from both sides: x + 5 - 3 = 10 - 3.

Step 3: Simplify: x + 2 = 7.

Method 2: Column Method

When subtracting while maintaining equality using the column method, align the expressions vertically. Make sure to subtract the same value from both sides and combine like terms.

For example, Subtract 4 from both sides of the equation 2x + 3 = 11.

Solution: Arrange the equation vertically: 2x + 3 ← Left side - 4 ← Subtracted value ---------- 2x - 1 = 7

In algebra, subtraction while maintaining equality has several properties:

1. Subtraction must maintain balance To keep an equation balanced, any operation performed on one side must be performed on the other.
2. Subtraction is not commutative In maintaining equality, the order of operations matters.
3. Subtraction is not associative Operations performed in different groupings can lead to different results.
4. Subtraction of zero Subtracting zero from an equation does not change its balance: A - 0 = A

These tips can help students efficiently subtract while maintaining equality:

Tip 1: Always perform the same operation on both sides to maintain balance.

Tip 2: Double-check the signs when subtracting to prevent errors.

Tip 3: Use the column method for visual clarity, especially with complex equations.

Subtracting while maintaining equality can be challenging, often leading to common mistakes. Awareness of these errors can help students avoid them.