Solve for m. 4/3 m = -m + 5/3 m + 3 m = _____________.

To solve for ( m ) in the equation

[

frac{4}{3} m = -m + frac{5}{3} m + 3,

]

let’s first combine the terms on the right side of the equation. You can rewrite (-m) as (-frac{3}{3} m) so they have a common denominator:

[

frac{4}{3} m = -frac{3}{3} m + frac{5}{3} m + 3.
]

Now simplify the right side:

[

frac{4}{3} m = left(-frac{3}{3} m + frac{5}{3} mright) + 3 = frac{2}{3} m + 3.
]

Next, subtract (frac{2}{3} m) from both sides:

[

frac{4}{3} m – frac{2}{3} m = 3.
]

This simplifies to:

[

frac{2}{3} m = 3.
]

To isolate ( m ), multiply both sides by (frac{3}{2}):

[

m = 3 times frac{3}{2} = frac{9}{2}.

]

Thus, the solution is

[

m = frac{9}{2}.

]