Home › NY Regents Algebra I › Mathematics › Solving Linear Equations and Inequalities › Solve: 6 = (1/2)v + (2/5)v - (3/4)v.
Solve: 6 = (1/2)v + (2/5)v - (3/4)v.
Av = 20
Bv = 40
Cv = -40
Dv = 8
Answer & Solution
Correct answer: B. v = 40
1. Find the LCD of the fractions one-half, two-fifths, and three-fourths, which is 20.
2. Multiply every term on both sides by 20 to clear the fractions: 120 equals 10v plus 8v minus 15v.
3. Combine like terms on the right: 10v plus 8v minus 15v simplifies to 3v.
4. Divide both sides by 3 to get v equals 40, and checking confirms one-half of 40, plus two-fifths of 40, minus three-fourths of 40, equals 6.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.5 Solve Equations with Fractions or Decimals_
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