alleryStart learning →Solve for x: 7 = (1/2)x + (3/4)x - (2/3)x.
Ax = 12
Bx = 84
Cx = 7
Dx = 6
Answer & Solution
Correct answer: A. x = 12
1. Clear the fractions by multiplying both sides by the LCD of 2, 4, and 3, which is 12.
2. The left side becomes 12 x 7 = 84.
3. The right side becomes 6x + 9x - 8x.
4. Combine like terms: 6x + 9x - 8x = 7x, so 84 = 7x.
5. Divide both sides by 7: x = 12.
6. Check: (1/2)(12) + (3/4)(12) - (2/3)(12) = 6 + 9 - 8 = 7, a true statement.
7. x = 84 is the trap of stopping after multiplying by the LCD, and x = 7 just echoes the constant from the question.
_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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