Chapter 21: Chapter 21

Problem 625

Remove fractional coefficients from the equation $2 \mathrm{x}^{3}-(2 / 3) \mathrm{x}^{2}-(1 / 8) \mathrm{x}+(3 / 16)=0$

Short Answer

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To remove the fractional coefficients from the equation $2x^3 - (\frac{2}{3})x^2 - (\frac{1}{8})x + (\frac{3}{16}) = 0$, find the least common denominator (LCD) of the fractions, which is 24. Then, multiply the entire equation by the LCD and distribute it to each term: $48x^3 - 16x^2 - 3x + 4.5 = 0$. The equivalent equation without fractions is $48x^3 - 16x^2 - 3x + 4.5 = 0$.

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identify the fractions and their denominators

First, we need to identify the fractional coefficients in the given equation and their respective denominators: $2x^3 - (\frac{2}{3})x^2 - (\frac{1}{8})x + (\frac{3}{16}) = 0$ The fractions are $\frac{2}{3}$, $\frac{1}{8}$, and $\frac{3}{16}$, and their denominators are 3, 8, and 16.

Step 2: Find the least common denominator (LCD)

Now, we need to find the least common denominator (LCD) of the three identified denominators, which is the smallest positive integer divisible by the three denominators. The prime factors of the denominators are: 3: $\underline{3}$ 8: 2 × 2 × $\underline{2}$ 16: 2 × 2 × 2 × $\underline{2}$ Taking the highest power of each prime factor present in the prime factorizations, the LCD is: LCD = 2³ × 3 = 24

Step 3: Multiply the equation by the LCD

Now, we will multiply the entire equation by the LCD, which is 24: 24(2x³ - ($\frac{2}{3}$x² - $\frac{1}{8}$x + $\frac{3}{16}$) = 24 × 0

Step 4: Distribute the LCD

Next, distribute the LCD to each term in the equation: 48x³ - $\frac{2}{3}$ × 24x² - $\frac{1}{8}$ × 24x + $\frac{3}{16}$ × 24 = 0 Simplify the fractions and multiply: 48x³ - 16x² - 3x + 4.5 = 0

Step 5: Rewrite the equation without fractions

Now, we have an equation without fractions as desired: 48x³ - 16x² - 3x + 4.5 = 0 The given equation with fractional coefficients has been transformed into an equivalent equation with no fractions.

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Chapter 21: Chapter 21

Remove fractional coefficients from the equation $2 \mathrm{x}^{3}-(2 / 3) \mathrm{x}^{2}-(1 / 8) \mathrm{x}+(3 / 16)=0$

Short Answer

Step by step solution

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Step 1: Identify the fractions and their denominators

Step 2: Find the least common denominator (LCD)

Step 3: Multiply the equation by the LCD

Step 4: Distribute the LCD

Step 5: Rewrite the equation without fractions

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Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

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Chapter 12

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Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

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Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

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Chapter 33

Chapter 34

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Chapter 38

Chapter 39

Chapter 40

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Chapter 42

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