Question

Solve equation and check solution. 1/2(x+2) -1/3(x-1)=1/2(x+1)

Answer 1

Starting from the equation:

`(1)/(2)(x+2)-(1)/(3)(x-1)=(1)/(2)(x+1)`

Notice that the coefficients of the binomials are 1/2, -1/3 and 1/2. The least common multiple of 2 and 3 is 6. Multiply both sides of the equation by 6 to get rid of all the denominators:

`\begin{gathered} 6*\lbrack(1)/(2)(x+2)-(1)/(3)(x-1)\rbrack=6*\lbrack(1)/(2)(x+1)\rbrack \\ \Rightarrow6*(1)/(2)(x+2)-6*(1)/(3)(x-1)=6*(1)/(2)(x+1) \\ \Rightarrow3(x+2)-2(x-1)=3(x+1) \end{gathered}`

Use the distributive property to expand all the parentheses:

`\begin{gathered} \Rightarrow3x+3*2-2x-2*-1=3x+3*1 \\ \Rightarrow3x+6-2x+2=3x+3 \end{gathered}`

Combine like terms on the left member of the equation: