Question

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

Answer 1

Starting from the equation:

$\frac{1}{2}(x+2)-\frac{1}{3}(x-1)=\frac{1}{2}(x+1)$

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:

$\begin{gathered} 6\times\lbrack\frac{1}{2}(x+2)-\frac{1}{3}(x-1)\rbrack=6\times\lbrack\frac{1}{2}(x+1)\rbrack \\ \Rightarrow6\times\frac{1}{2}(x+2)-6\times\frac{1}{3}(x-1)=6\times\frac{1}{2}(x+1) \\ \Rightarrow3(x+2)-2(x-1)=3(x+1) \end{gathered}$

Use the distributive property to expand all the parentheses:

$\begin{gathered} \Rightarrow3x+3\times2-2x-2\times-1=3x+3\times1 \\ \Rightarrow3x+6-2x+2=3x+3 \end{gathered}$

Combine like terms on the left member of the equation:

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