Answer:
[tex]\boxed{\boxed{\sf x=\frac{9}{4} }\:\sf or \:\boxed{x=2.25}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{1}{2}\:x+\cfrac{3}{4}=\:x\cfrac{5}{6}[/tex]
Subtract x (5/6) from both sides:
[tex]\longmapsto\sf \cfrac{1}{2}\: x+\cfrac{3}{4} -x\left(\cfrac{5}{6}\right)=0[/tex]
Subtract 3/4 from both sides:
** Anything subtracted from zero gives its negation.**
[tex]\longmapsto\sf -\cfrac{1}{3}\:x=-\cfrac{3}{4}[/tex]
Multiply both sides by -3, reciprocal of - 1/3
[tex]\longmapsto\sf x=-\cfrac{3}{4} (-3)[/tex]
Express - 3/4 (-3) as single fraction:
[tex]\longmapsto\sf x=\cfrac{-3(-3)}{4}[/tex]
Multiply -3 and -3 = 9
[tex]\longmapsto\sf x= \cfrac{9}{4}[/tex]
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