Question

2/9(x+2)+1/4=1/2(5-3x). How do you solve this?

Answer 1

Begin by getting rid of x in the denominators. Multiply through (everything on both sides of the equation) by x+2. Then do the same with 5-3x. Multiply everything out, gather like terms, and you'll have something you can solve.

Answer 2

I don't understand. Can you please show me?

Answer 3

\[\frac{ 2 }{ 9(x+2) }+\frac{ 1 }{ 4 }=\frac{ 1 }{ 2(5-3x) }\]I assume this is the starting point. Now multiply through by x+2:\[\frac{ 2 }{ 9 }+\frac{ x+2 }{ 4 }=\frac{ x+2 }{ 2(5-3x) }\]Do you see how this worked? Multiplying the first fraction times x+2 eliminated that factor from the denominator. The other two fractions now have x+2 in the numerator. Now multiply through by 5-3x:\[\frac{ 2(5-3x) }{ 9 }+\frac{ (x+2)(5-3x) }{ 4 }=\frac{ x+2 }{ 2 }\]You still have fractions, so you can multiply through again by 36 to get rid of them. Then expand the results, gather terms and solve the resulting quadratic equation.