15. Construct Arguments Mapgie suid that she could add 8 te both sides of any equation and the exprestions on tooth sides of the equation would still be equilh. Do you agree? Explain.

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UpStudy AI · Accepted Answer

Yes, I agree with Mapgie's statement. Adding the same number to both sides of an equation preserves the equality between the two expressions. This principle is a fundamental property of equations in algebra known as the **Addition Property of Equality**.

### **Understanding the Addition Property of Equality**

The **Addition Property of Equality** states that if you add the same number to both sides of an equation, the equality remains true. Mathematically, this can be expressed as:

$$
\text{If } a = b, \text{ then } a + c = b + c
$$

where $$ a $$ and $$ b $$ are expressions or numbers, and $$ c $$ is any real number.

### **Why This Property Holds True**

Consider the original equation:

$$
a = b
$$

If you add the same number $$ c $$ to both sides:

$$
a + c = b + c
$$

Since both sides started as equal and you've performed the same operation (adding $$ c $$) to each side, the equality remains intact. The balance of the equation is maintained because both sides increase by the same amount.

### **Example**

Let's take a simple equation:

$$
5 = 5
$$

Now, add 8 to both sides:

$$
5 + 8 = 5 + 8 \
13 = 13
$$

The equation remains balanced and true.

### **Why It's Important**

This property is essential for solving equations because it allows us to isolate variables. By performing the same operation on both sides, we can manipulate the equation to find the value of the unknown variable without altering the equality.

### **Conclusion**

Mapgie is correct in her assertion. Adding the same number to both sides of an equation is a valid operation that maintains the equality of the two expressions. This principle is a cornerstone in algebra for simplifying and solving equations.
Yes, adding the same number to both sides of an equation keeps both sides equal.

Construct Arguments Mapgie suid that
she could add 8 te both sides of any
equation and the exprestions on tooth sides
of the equation would still be equilh. Do you
agree? Explain.

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