Solve Equations with Fraction or Decimal Coefficients: example 8.39

Solve: $x + \frac{1}{3} = \frac{1}{6} x - \frac{1}{2} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $a + \frac{3}{4} = \frac{3}{8} a - \frac{1}{2} .$

How did it go?

Find the LCD of all the fractions in the equation.
Multiply both sides by the LCD.
Distribute.
Simplify — no more fractions!
Subtract $x$ from both sides.
Simplify.
Subtract 2 from both sides.
Simplify.
Divide by 5.
Simplify.
Check: Substitute $x = −1 .$

Find the LCD of all the fractions in the equation.
Multiply both sides by the LCD.
Distribute.
Simplify — no more fractions!
Subtract $x$ from both sides.
Simplify.
Subtract 2 from both sides.
Simplify.
Divide by 5.
Simplify.
Check: Substitute $x = −1 .$