To solve the equation below:
[tex]\frac{1}{3}(5+7x)=12-\frac{1}{2}(3-2x)[/tex]eliminate the denominators by multiplying each term on both sides of the equation by the least common denominator or the LCD. In this case, since the least common multiple of 3 and 2 is 6, the LCD must be 6.
[tex]\begin{gathered} 6\lbrack\frac{1}{3}(5+7x)\rbrack=6\lbrack12-\frac{1}{2}(3-2x)\rbrack \\ 6\lbrack\frac{1}{3}(5+7x)\rbrack=6\lbrack12\rbrack-6\lbrack\frac{1}{2}(3-2x)\rbrack \\ 2(5+7x)=72-3(3-2x) \end{gathered}[/tex]Eliminate the parentheses by distributing the numerical values outside the parentheses. In this case, we distribute the 2 to 5 and 7x and then distribute -3 to 3 and -2x.
[tex]\begin{gathered} 2(5)+2(7x)=72-3(3)-3(-2x) \\ 10+14x=72-9+6x \end{gathered}[/tex]Simplify both sides of the equation by combining like terms. Like terms are the terms with the same literal coefficients.
[tex]10+14x=63+6x[/tex]Isolate the variable terms by subtracting 6x and 10 from both sides of the equation.
[tex]\begin{gathered} 10+14x-6x-10=63+6x-6x-10 \\ 8x=53 \end{gathered}[/tex]Solve for x by dividing both sides of the equation by 8.
[tex]\begin{gathered} \frac{8x}{8}=\frac{53}{8} \\ x=\frac{53}{8} \end{gathered}[/tex]Therefore, the value of x must be 53/8.
