Question

Which expressions are equivalent to (1/3x+x−5/3x)−(−4/3x+2) ?

Select all correct answers.
A. −2−x+2x
B. x−2
C. 2−x
D. −2+x−2x

Answer 1

The expression (1/3x + x - 5/3x) - (-4/3x + 2) simplifies to x - 2. Therefore, the equivalent expression is 'x - 2' (option B).

Step-by-step explanation:

The question asks which expressions are equivalent to the simplified form of the expression given by (1/3x + x - 5/3x) - (-4/3x + 2). We need to combine like terms and simplify the expression step by step.

• First, combine the x terms: (1/3x + x - 5/3x) = (1/3x - 5/3x) + x = -4/3x + x
• Now, simplify the expression by distributing the subtraction across the second set of parentheses: -(-4/3x + 2) = 4/3x - 2
• Add the results of step 1 and step 2: (-4/3x + x) + (4/3x - 2) = x - 2

Through these steps, we find that the original expression simplifies to x - 2. Hence, the equivalent expression to the original is B. x - 2.