Question

1. solve the equation $2x + 4\frac{1}{5} = 9$. explain the steps and properties you used.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(4\frac{1}{5}\) to an improper fraction. \(4\frac{1}{5}=\frac{4\times5 + 1}{5}=\frac{21}{5}\). So the equation becomes \(2x+\frac{21}{5}=9\).

Step2: Subtract \(\frac{21}{5}\) from both sides (Subtraction Property of Equality)

Subtract \(\frac{21}{5}\) from both sides: \(2x+\frac{21}{5}-\frac{21}{5}=9 - \frac{21}{5}\). Simplify the left side to \(2x\). For the right side, convert \(9\) to fifths: \(9=\frac{45}{5}\), so \(\frac{45}{5}-\frac{21}{5}=\frac{24}{5}\). Now the equation is \(2x=\frac{24}{5}\).

Step3: Divide both sides by 2 (Division Property of Equality)

Divide both sides by \(2\): \(x=\frac{24}{5}\div2\). Dividing by \(2\) is the same as multiplying by \(\frac{1}{2}\), so \(x=\frac{24}{5}\times\frac{1}{2}=\frac{12}{5}\) (or \(2\frac{2}{5}\)).

Answer:

\(x = \frac{12}{5}\) (or \(x = 2\frac{2}{5}\))