Question

Identify as an expression or an equation. Then perform the operation or solve the equation.

Answer 1

Given:

`(2)/(5)x-(7)/(10)x=1`

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

`\begin{gathered} Example\text{ is;} \\ 3x-2 \end{gathered}`

An equation is made up of two expressions connected by an equal sign.

`\begin{gathered} Example\text{ is;} \\ 2x+5=10x+3 \end{gathered}`

Hence,

`\begin{gathered} (2)/(5)x-(7)/(10)x=1 \\ \\ This\text{ represents an equation because it has equality sign.} \\ \\ The\text{ solution is gotten by solving further for x;} \\ (2)/(5)x-(7)/(10)x=1 \\ Multiplying\text{ through by the least common denominator \lparen LCD\rparen, the LCD is 10} \\ Thus, \\ ((2x)/(5)*10)-((7x)/(10)*10)=1*10 \\ 4x-7x=10 \\ -3x=10 \\ Dividing\text{ both sides by -3,} \\ x=(10)/(-3) \\ x=-(10)/(3) \\ \\ As\text{ a mixed number,} \\ x=-3(1)/(3) \end{gathered}`

Therefore, the answer is;

`It\text{ is an equation, and the solution set is }\lbrace-3(1)/(3)\rbrace`