Evaluate 𝑓 of five-sevenths given that 𝑓 of 𝑥 equals three 𝑥 plus three-fourths.
To solve this problem, we’ll need to substitute our five-sevenths in for 𝑥. The substitutions would look like this. Now we need to evaluate this equation. We’ll start by multiplying three times five-sevenths. We know that that means we’ll need to multiply three times the numerator five: three times five over seven, which gives us 15 sevenths.
Then, we can bring down our three-fourths. Now, we’ll need to add these two fractions together. The problem is they don’t have a common denominator. So before we can add them together, we’ll need to find a common denominator of seven and four. The least common multiple of seven and four equals 28. This means that we’ll use 28 as our common denominator. To move from seven to 28, we’ll multiply it by four.
And since we multiplied by four on the denominator, we’ll need to multiply by four in the numerator. Multiplying 15 by four, which equals 60. To move from four to 28, we multiply it by seven. This means we need to multiply our numerator by seven as well. Three times seven equals 21. Okay, now that our fractions have a common denominator, we can go ahead and add. Sixty twenty-eighths plus twenty-one twenty-eighths equals eighty-one twenty-eighths.
Now, we’ll need to convert this improper fraction to a mixed number. We need to divide 81 by 28, and it goes in two times. Two times 28 equals 56, and there is a remainder of 25. This means we can convert eighty-one twenty-eighths into two and 25 over 28. The function of five-sevenths would be equal to two and 25 over 28.