College Algebra (11th Edition)

x = $\frac{5}{12}$
1. The first step we want to take is to clear the fractions in this linear equation. To clear fractions, we want to use the distributive property and distribute the least common denominator. To find the least common denominator we want to list the multiples of each number in the denominators involved until we find the first multiple that each denominator has in common. This is called the least common denominator. factors of 4: 4, 8, 12, 16, 20,... factors of 5: 5, 10, 15, 20, 25... factors of 2: 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20,... The smallest number these three lists have in common is 20. We will use this number to distribute to the entire equation and clear the fractions. $\frac{7}{4} + \frac{1}{5}x - \frac{3}{2} = \frac{4}{5}x$ $20(\frac{7}{4} + \frac{1}{5}x - \frac{3}{2} = \frac{4}{5}x)$ $35 + 4x - 30 = 16x$ 2. Next, we want to combine the like terms 35 and -30. $4x + 5 = 16x$ 3. Next, subtract 4x from both sides of the equation to isolate the variable. $5 = 12x$ 4. And finally, divide both sides by 12 to solve for x. $x = \frac{5}{12}$