Solve Equations with Fraction or Decimal Coefficients: example 8.38

Solve: $7 = \frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x .$

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: $6 = \frac{1}{2} v + \frac{2}{5} v - \frac{3}{4} v .$

How did it go?

Find the least common denominator of all the fractions in the equation.
Multiply both sides of the equation by 12.
Distribute.
Simplify — and notice, no more fractions!
Combine like terms.
Divide by 7.
Simplify.
Check: Let $x = 12 .$

Find the least common denominator of all the fractions in the equation.
Multiply both sides of the equation by 12.
Distribute.
Simplify — and notice, no more fractions!
Combine like terms.
Divide by 7.
Simplify.
Check: Let $x = 12 .$