This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's simplify these algebraic expressions. Problem 1: Simplify 4(m+n) - 3(2m-n) + (m-3n) Step 1: Distribute the coefficients into the parentheses. 4m + 4n - 6m + 3n + m - 3n Step 2: Group the like terms together. (4m - 6m + m) + (4n + 3n - 3n) Step 3: Combine the like terms. (4 - 6 + 1)m + (4 + 3 - 3)n (-2 + 1)m + (7 - 3)n -1m + 4n -m + 4n Problem 2: Express (K-2e)/(2) - (K-3e)/(8) as a single fraction in simplest form. Step 1: Find the least common denominator (LCD) for the fractions. The denominators are 2 and 8. The LCD is 8. To get a denominator of 8 for the first fraction, multiply it by (4)/(4). (4(K-2e))/(4 · 2) - (K-3e)/(8) (4(K-2e))/(8) - (K-3e)/(8) Step 2: Combine the numerators over the common denominator. Remember to distribute the negative sign to all terms in the second numerator. (4(K-2e) - (K-3e))/(8) Step 3: Distribute the 4 and the negative sign in the numerator. (4K - 8e - K + 3e)/(8) Step 4: Combine like terms in the numerator. ((4K - K) + (-8e + 3e))/(8) (3K - 5e)/(8) (3K - 5e)/(8) That's 2 down. 3 left today — send the next one.