Answer:
The value of x in the given equation is [tex]-\frac{13}{3}[/tex]
That is [tex]x=\frac{-13}{3}[/tex]
Step-by-step explanation:
Given equation is [tex]\frac{-8}{3}x+4(x+\frac{9}{4})=\frac{-2}{3}(x+\frac{12}{8})+3[/tex]
To simply the given equation as below :
[tex]\frac{-8}{3}x+4(x+\frac{9}{4})=\frac{-2}{3}(x+\frac{12}{8})+3[/tex]
[tex]\frac{-8}{3}x+4(x+\frac{9}{4})=\frac{-2}{3}(x+4)+3[/tex]
[tex]\frac{-8}{3}x+4x+9=\frac{-2}{3}x+(\frac{-2}{3})(4)+3[/tex] ( applying the distributive property )
[tex]\frac{-8}{3}x+4x+9=\frac{-2}{3}x+(\frac{-2}{3})(4)+3[/tex]
[tex]\frac{-8}{3}x+4x+9=\frac{-2}{3}x+\frac{-8}{3}+3[/tex]
[tex]\frac{-8x+12x}{3}+9=\frac{-2}{3}x+\frac{-8+9}{3}[/tex]
[tex]\frac{4x}{3}+9=\frac{-2}{3}x+\frac{1}{3}[/tex]
[tex]\frac{4x}{3}+9-(\frac{-2}{3}x+\frac{1}{3})=\frac{-2}{3}x+\frac{1}{3}-(\frac{-2}{3}x+\frac{1}{3})[/tex]
[tex]\frac{4x}{3}+9+\frac{2}{3}x-\frac{1}{3}=0[/tex]
[tex]\frac{6x}{3}+9-\frac{1}{3}=0[/tex]
[tex]\frac{6x+27-1}{3}=0[/tex]
[tex]\frac{6x+26}{3}=0[/tex]
6x+26=0
6x=-26
[tex]x=-\frac{26}{6}[/tex]
[tex]x=-\frac{13}{3}[/tex]
Therefore the value of x is [tex]-\frac{13}{3}[/tex]
That is [tex]x=\frac{-13}{3}[/tex]
