Problem 112 - Introductory Algebra for College Students

Question

Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable \(x\) represent the number. The product of \(\frac{3}{4}\) and a number increased by 9

Step-by-Step Solution

Answer

The translated algebraic expression is \(\frac{3x}{4} + 9\)

Step 1: Identifying the variable

Firstly, realize that the variable 'x' is representing the unknown number. This problem involves doing operations with this unknown number.

Step 2: Translating 'the product of \(\frac{3}{4}\) and a number'

From this phrase, you must multiply \(\frac{3}{4}\) by the number (which we've defined as \(x\)). This leads to \(\frac{3}{4}x \) or \(\frac{3x}{4}\), both of which mean the same thing and can be used interchangeably.

Step 3: Translating 'increased by 9'

This phrase means that you are to add 9. This part of the phrase brings '+9' to the expression we have formed already in Step 2. Thus the full expression becomes: \(\frac{3x}{4} + 9\)