Question

1. the area of the rectangle is (18x - 12) square inches. write an expression that represents the length of the rectangle (in inches). 6 in.

Explanation:

Step1: Recall the area formula of a rectangle

The area formula of a rectangle is \(A = lw\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We know \(A=(18x - 12)\) square inches and \(w = 6\) inches. So, \(l=\frac{A}{w}\).

Step2: Substitute the values into the formula

Substitute \(A=(18x - 12)\) and \(w = 6\) into \(l=\frac{A}{w}\), we get \(l=\frac{18x-12}{6}\).

Step3: Simplify the expression

Use the distributive property of division \(\frac{a - b}{c}=\frac{a}{c}-\frac{b}{c}\). So, \(\frac{18x-12}{6}=\frac{18x}{6}-\frac{12}{6}\).
Since \(\frac{18x}{6}=3x\) and \(\frac{12}{6} = 2\), the simplified expression is \(3x-2\).

Answer:

\(3x - 2\)