Question

Annie said that she simplified the expression 6.5(x+0.5x+1) by writing the equivalent expression 6.5x+3.25x+6.5.

Answer 1

Annie incorrectly simplified the expression by not combining like terms. After correctly distributing 6.5, the terms should be combined to yield 9.75x + 6.5 as the simplified expression.

Step-by-step explanation:

Annie simplified the expression 6.5(x+0.5x+1) incorrectly. Correct simplification involves combining like terms. First, factor out common terms: 6.5x + 6.5(0.5x) + 6.5(1). Then, simplify by multiplying each term inside the parentheses by 6.5: 6.5x + 3.25x + 6.5. However, she failed to combine the x terms. The correct final expression after combining like terms should be 9.75x + 6.5. This is because 6.5x + 3.25x equals 9.75x, which simplifies the original expression.

Answer 2

Answer: No although the expressions are equivalent by the distribute property, it is not in simplest form because when we combine 6.5x and 3.25x as they are like terms the simplified expression is 9.75x + 6.5

Step-by-step explanation: hope this helps