Fractional linear equations

10 = 3 over 5 (x+5)

At first glance I believe you meant 10 = (3/5) (x+5). It's important that you share the instructions for each problem you post; I assume they state: "solve the following fractional linear equation for x."

Here are two approaches. Take your pick.

1) Distribute the multiplier (3/5) over (x+5). Resulting equation is

10 = (3/5) x + 3. Subtr. 3 from both sides: 7 = (3/5) x. Mult both sides by (5/3). Result: (35/3) = x.

2) Mult. the original equation by 5 to remove fractions: 50=3 (x+5). Multiply out 3 (x+5), to obtain 50=3x + 15. Subtr. 15 from both sides. Result:

35=3x. Divide both sides by 3.