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Solving Equations with Decimals and Fractions: Step-by-Step Examples

This guide presents a comprehensive approach to solving equations that involve decimals and fractions. Illustrated with detailed examples, we simplify equations like (1.4x - 1.8 + 2.35x = 0.21) by clearing decimals and combining like terms. We also explain how to handle fractions by multiplying through by the least common denominator (LCD) to simplify the process. Gain confidence in your algebra skills with our guided practice problems that put your understanding to the test.

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Solving Equations with Decimals and Fractions: Step-by-Step Examples

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  1. 375x 201 = 375 375 Solving an Equation Involving Decimals EXAMPLE 2 1.4x –1.8 + 2.35x = 0.21 Original equation. (1.4x –1.8 + 2.35x)100 = (0.21)100 Multiply each side by 100 to clear decimals. 140x–180 + 235x= 21 Simplify. 375x–180 = 21 Combine like terms. 375x = 201 Add 180 to each side. Divide each side by 375. x = 0.536 Simplify.

  2. 3 1 7 x x – = + 10 6 10 ) ) ( ( 3 7 1 x x 30 – 30 = + 10 10 6 ) ) ( ( ( 3 7 1 ) x x 30 – 30 30 = + 10 10 6 3 5 3 3 30 1 30 7 30 x x – + = 10 10 6 1 1 1 21 3 1 , or 1 x= = 14 2 2 Solving an Equation Involving Fractions EXAMPLE 3 Original equation. Multiply each side by the LCD, 30. Distributive property Divide out common factors. 9x = –5x + 21 Simplify. 14x = 21 Add 5xto each side. Divide each side by 14. Simplify.

  3. 2. – 1.7k + 6.7k = 13.1 for Examples 2 and 3 GUIDED PRACTICE Solve the equation. k = 2.62

  4. 3. 1.2n – 0.24= 0.7n for Examples 2 and 3 GUIDED PRACTICE 0.48 = n

  5. 8.3– 8y = 1.2y +6 4. for Examples 2 and 3 GUIDED PRACTICE 0.25 = y

  6. 5. 4 7 x – + 3 = 5 10 –37 x = 8 for Examples 2 and 3 GUIDED PRACTICE

  7. 1 1 s 2s –1 = 4 3 s = 4 9 for Examples 2 and 3 GUIDED PRACTICE 6.

  8. v v + = –15 4 or v –1 = 11 11 3 5 5 8 6 8 for Examples 2 and 3 GUIDED PRACTICE 7.

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