Final answer:
The algebraic expression -4/7 + 2/3x - 14x + 4/7 simplifies to -40/3x after combining like terms and ensuring they have a common denominator.
Step-by-step explanation:
To simplify the algebraic expression -4/7 + 2/3x - 14x + 4/7, you need to combine like terms and arrange the terms in a standard form. First, combine the constant fractions: -4/7 + 4/7 = 0 (since they are additive inverses of each other). Next, combine the variable terms: 2/3x - 14x. You can't directly combine these terms since they don't have the same denominator, but you can write -14x as -14/1 x. Now, you can look for a common denominator for 2/3 and -14/1, which is 3. Multiply -14/1 by 3/3 to get the common denominator: -14/1 x * 3/3 = -42/3 x. Now combine the variable terms with the common denominator: 2/3x - 42/3x = -40/3x. The simplified expression is: -40/3x. Remember to always check if the simplified form is reasonable by ensuring that all like terms are correctly combined.