Respuesta :
Given the following equation:
[tex]\frac{2}{3}x-1=2(y+7)[/tex]You can solve for "y" in term of "x" applying the following steps:
1. You must apply the Distributive property, which states that
[tex]\begin{gathered} a(b+c)=ab+ac \\ a(b-c)=ab-ac \end{gathered}[/tex]Then:
[tex]\begin{gathered} \frac{2}{3}x-1=(2)(y)+(2)(7) \\ \\ \frac{2}{3}x-1=2y+14 \end{gathered}[/tex]2. Now you can apply the the Substraction property of equality by subtracting 14 from both sides of the equation:
[tex]\begin{gathered} \frac{2}{3}x-1-(14)=2y+14-(14) \\ \\ \frac{2}{3}x-15=2y \end{gathered}[/tex]3. Apply the Division property fo equality by dividing both sides of the equation by 2:
[tex]\begin{gathered} \frac{2}{3\cdot2}x-\frac{15}{2}=\frac{2y}{2} \\ \\ \frac{2}{6}x-\frac{15}{2}=y \\ \\ \frac{1}{3}x-\frac{15}{2}=y \end{gathered}[/tex]The answer is:
[tex]y=\frac{1}{3}x-\frac{15}{2}[/tex]