Problem 114 - 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 \(9,\) is 2 less than the number.

Step-by-Step Solution

Answer

The algebraic equation for the given English phrase is \(\frac{3}{4}x + 9 = x - 2\).

Step 1: Identify the variable

The exercise mentions that 'Let the variable \(x\) represent the number'. So, the number being referred to will be represented by \(x\).

Step 2: Translate 'Product of \(\frac{3}{4}\) and a number'

'Product' signifies multiplication in mathematics. Therefore, 'the product of \(\frac{3}{4}\) and a number' translates to \(\frac{3}{4} \times x\).

Step 3: Translate 'increased by \(9\)'

'Increased by' signifies addition. Adding 9 to the product gives us the expression: \(\frac{3}{4}x + 9\).

Step 4: Translate 'is 2 less than the number'

'Is 2 less than the number' represents the number subtracted by 2, which gives us the expression: \(x - 2\). This is the right side of the equation.

Step 5: Form the final equation

Combining all the parts, we get the final equation as \(\frac{3}{4}x + 9 = x - 2\).