Final answer:
To solve the equation 2x + 4 1/5 = 9, you should isolate the variable x. Start by subtracting 4 1/5 from both sides to get 2x = 24/5. Then, divide both sides by 2 to find x = 12/5.
Step-by-step explanation:
To solve the equation 2x + 4 1/5 = 9, we need to isolate the variable x. Let's start by subtracting 4 1/5 from both sides of the equation, which gives us 2x = 9 - 4 1/5. To subtract the mixed number, we need to convert it to an improper fraction. 4 1/5 is equivalent to 21/5. So, the equation becomes 2x = 9 - 21/5. Next, we need to simplify the right side of the equation by finding a common denominator. The common denominator for 5 and 1 is also 5. Therefore, 9 - 21/5 = 45/5 - 21/5 = (45 - 21)/5 = 24/5. So, the equation is now 2x = 24/5.
To solve for x, we divide both sides of the equation by 2: 2x/2 = 24/5 / 2. Dividing a fraction by a whole number is equivalent to multiplying the fraction by the reciprocal of the whole number. So, the equation becomes x = (24/5) * (1/2). Multiplying fractions is done by multiplying the numerators (top numbers) and denominators (bottom numbers). So, x = 24/5 * 1/2 = (24 * 1) / (5 * 2) = 24/10. Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case. So, the final answer is x = 12/5.
The student asked to solve the equation 2x + 4 1/5 = 9. To do this, we would first subtract 4 1/5 from both sides to isolate the variable term:
Subtract 4 1/5 from both sides: 2x + 4 1/5 - 4 1/5 = 9 - 4 1/5.
Simplify the right side by converting 4 1/5 to an improper fraction (21/5) and subtracting from 9 (which is 45/5 when converted to a fraction with the same denominator as 21/5): 45/5 - 21/5 = 24/5.
The equation is now 2x = 24/5. To solve for x, divide both sides by 2: x = (24/5) / 2.
Upon simplifying, we get x = 24/5 * 1/2 = 24/10 = 2.4.
Thus, the solution to the equation is x = 2.4.