Solution:
Given:
[tex]\frac{2}{5}x-\frac{7}{10}x=1[/tex]
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
[tex]\begin{gathered} Example\text{ is;} \\ 3x-2 \end{gathered}[/tex]
An equation is made up of two expressions connected by an equal sign.
[tex]\begin{gathered} Example\text{ is;} \\ 2x+5=10x+3 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \frac{2}{5}x-\frac{7}{10}x=1 \\ \\ This\text{ represents an equation because it has equality sign.} \\ \\ The\text{ solution is gotten by solving further for x;} \\ \frac{2}{5}x-\frac{7}{10}x=1 \\ Multiplying\text{ through by the least common denominator \lparen LCD\rparen, the LCD is 10} \\ Thus, \\ (\frac{2x}{5}\times10)-(\frac{7x}{10}\times10)=1\times10 \\ 4x-7x=10 \\ -3x=10 \\ Dividing\text{ both sides by -3,} \\ x=\frac{10}{-3} \\ x=-\frac{10}{3} \\ \\ As\text{ a mixed number,} \\ x=-3\frac{1}{3} \end{gathered}[/tex]
Therefore, the answer is;
[tex]It\text{ is an equation, and the solution set is }\lbrace-3\frac{1}{3}\rbrace[/tex]
