Problem 73 - Introductory Algebra for College Students

Question

State the multiplication property of equality and give an example.

Step-by-Step Solution

Answer

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the two sides remain equal. An example is, for the equation \(2x = 10\), we can multiply both sides of the equation by \(.5\) to get \(x = 5\).

Step 1: State the Multiplication Property of Equality

The Multiplication Property of Equality states that if you multiply any number or expression on both sides of an equation by the same non-zero number, the two sides remain equal. This is used to adjust equations to help find the unknown values.

Step 2: Provide an Example

For example, suppose we have an equation, \(2x = 10\). To find the value of \(x\), we multiply both sides of the equation by the same number, in this case, \(0.5\) (which is the multiplicative inverse of \(2\)):\(0.5 * 2x = 0.5 * 10\)This simplifies to: \(x = 5\)Thus, \(x\) equals \(5\).