Problem 19 - Introductory Algebra for College Students

Question

Use the commutative property of multiplication to write an equivalent algebraic expression. $$7 x+23$$

Step-by-Step Solution

Answer

The equivalent expression using the commutative property of multiplication is \(x7 + 23\).

Step 1: Understanding the commutative property

The commutative property of multiplication states that for any real numbers \(a\) and \(b\), \(ab = ba\). This implies that the order of multiplying numbers (or variables) does not affect the result. In this exercise, the commutative property will be applied to an algebraic expression involving the variable \(x\).

Step 2: Applying the commutative property to the expression

The expression given is \(7x + 23\). There is only one term involving multiplication, which is \(7x\). From the commutative property, we can rearrange this term. Instead of \(7x\), we write \(x7\).

Step 3: Writing the final equivalent expression

Substituting \(x7\) back into the expression yields the equivalent expression \(x7 + 23\), which represents the same value as \(7x + 23\) for any value of \(x\).