Question

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

Explanation:

Step1: Subtract \( 4\frac{1}{5} \) from both sides

To isolate the term with \( x \), we use the subtraction property of equality. Subtract \( 4\frac{1}{5} \) (which is \( \frac{21}{5} \)) from both sides of the equation \( 2x + 4\frac{1}{5}=9 \). First, convert \( 9 \) to fifths: \( 9=\frac{45}{5} \). Then \( 2x=\frac{45}{5}-\frac{21}{5}=\frac{24}{5} \).

Step2: Divide both sides by 2

Using the division property of equality, divide both sides by \( 2 \) to solve for \( x \). Dividing \( \frac{24}{5} \) by \( 2 \) is the same as multiplying by \( \frac{1}{2} \), so \( x = \frac{24}{5}\times\frac{1}{2}=\frac{12}{5}=2\frac{2}{5} \).

Answer:

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