There we discussed about Solving Linear Equations by Transposition.
That knowledge is a prerequisite here.
Linear Equations with fractional and decimal coefficients
The fractions should be cleared by multiplying both sides of the equation by the Least Common Multiple (L.C.M.) of the denominators of the fractions in the equation.
Let us see a few examples.
Example 1 of Solving Rational Equations
Solve the Equation x⁄2 + x⁄3 = 5.
Solution: The given equation is x⁄2 + x⁄3 = 5. L.C.M. of the denominators 2 and 3 is 6. Multiplying both sides of the equation with 6, we get 6 x x⁄2 + 6 x x⁄3 = 6 x 5 ⇒ 3x + 2x = 30 ⇒ 5x = 30 ⇒ x = 30⁄5 = 6. Ans. Great Deals on School & Homeschool Curriculum Books
Example 2 of Solving Rational Equations
Solve the Equation x⁄3 - x⁄9 = 7x⁄6 - 17⁄3
Solution: The given equation is x⁄3 - x⁄9 = 7x⁄6 - 17⁄3 L.C.M. of the denominators 3, 6 and 9 is 18. Multiplying both sides of the equation with 18, we get 18 x x⁄3 - 18 x x⁄9 = 18 x 7x⁄6 - 18 x 17⁄3 ⇒ 6x - 2x = 3 x 7x - 6 x 17 ⇒ 4x = 21x - 102 ⇒ 4x - 21x = -102 ⇒ -17x = -102 ⇒ x = 6. Ans.
In case of decimals, multiply both sides with 10m Where m = the maximum number of digits after the decimal place.
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Solution: The given equation is 0.8x + 1.25 = 2x + 0.05 Here maximum number of digits after the decimal place are 2. ∴ multiplying both sides with 102i.e. 100, we get 100 (0.8x) + 100(1.25) = 100(2x) + 100(0.05) ⇒ 80x + 125 = 200x + 5 ⇒ 80x - 200x = 5 - 125 ⇒ -120x = -120 ⇒ x = 1. Ans.
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Solve the Equation (3x - 2)⁄3 + (2x + 3)⁄2 = x + 7⁄6
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