Question

Write an equivalent expression by distributing the "minus" sign outside the parentheses -(3.4n + 5p - 7.5)

Answer 1

Distributing the minus sign across -(3.4n + 5p - 7.5) results in the equivalent expression -3.4n - 5p + 7.5.

Step-by-step explanation:

The question asks to write an equivalent expression by distributing the "minus" sign outside of the parentheses in the expression -(3.4n + 5p - 7.5). Distribution of the minus sign means to multiply the inside of the parentheses by -1, therefore changing the sign of each term within the parentheses.

To distribute the minus sign across the parentheses, we perform the following steps:
1. Multiply 3.4n by -1, which gives us -3.4n.
2. Multiply 5p by -1, which results in -5p.
3. Multiply -7.5 by -1, yielding +7.5.

By combining these steps, the equivalent expression after distributing the minus sign becomes: -3.4n - 5p + 7.5.

Answer 2

An equivalent expression after distributing the "minus" sign outside the parentheses is -3.4n - 5p + 7.5.

In mathematics, equivalent expressions have the same value but may look different. They are essentially different ways of representing the same quantity. For example, \(2x + 3\) and \(x + x + 3\) are equivalent expressions because, for any value of \(x\), both expressions will result in the same numerical value.

Equivalent expressions can be obtained through various algebraic manipulations such as simplifying, factoring, or expanding. The key is that no matter what values you substitute for the variables, equivalent expressions will always yield the same result.

To distribute the "minus" sign outside the parentheses -(3.4n + 5p - 7.5), we need to apply the distributive property.

First, we can distribute the negative sign to each term inside the parentheses by changing the sign of each term.

So, -(3.4n + 5p - 7.5) becomes -3.4n - 5p + 7.5.