Respuesta :
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2[/tex]
To solve for the value of x, let's simplify the equation by eliminating the parenthesis first applying the distributative property.
[tex]-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex]The next step is to join similar terms on each side. Let's transfer -5/4x to the other side and -8 to the right side. In doing so, the signs will reverse as well. From positive to negative and vice versa.
[tex]\begin{gathered} -\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8 \\ \frac{5}{4}x=10 \end{gathered}[/tex]The last step is to divide both sides of the equation by 5/4 to solve for x.
[tex]\begin{gathered} \frac{\frac{5}{4}}{\frac{5}{4}}x=\frac{10}{\frac{5}{4}} \\ x=8 \end{gathered}[/tex]Therefore, the value of x is 8.
To check if it is correct, we can substitute the x value in the original equation by 8 and see if both sides are indeed equal.
[tex]\begin{gathered} -\frac{2}{3}(8+12)+\frac{2}{3}(8)=-\frac{5}{4}(8)+2 \\ -\frac{2}{3}(20)+\frac{16}{3}=-10+2 \\ -\frac{40}{4}+\frac{16}{3}=-8 \\ -\frac{24}{3}=-8 \\ -8=-8 \end{gathered}[/tex]Indeed both sides are equal therefore, the value of x must be 8.
