Question

Ahmed wrote the two expressions: Three-fourths (8x + 4) and 6x + 1. Which procedure can Ahmed follow to determine if the two expressions are equivalent?

Answer 1

Determine if the two expressions are equivalent by first expanding and simplifying the expression Three-fourths (8x + 4), then comparing the result to the second expression, 6x + 1. If both expressions yield the same result for all values of x, they are equivalent.

Step-by-step explanation:

To determine if the two expressions Three-fourths (8x + 4) and 6x + 1 are equivalent, Ahmed should follow these steps:

1. Expand the first expression by distributing the three-fourths across the terms inside the parentheses: \(\frac{3}{4}\) \(\times\) ((8x) + (4)).
2. Simplify the expression by multiplying each term within the parentheses by \(\frac{3}{4}\). This gives us (6x) + (3).
3. Compare the new expression (6x + 3) to the second expression (6x + 1) to see if they are identical.
4. If both expressions yield the same result for all values of x, they are equivalent. If not, they are not equivalent.
5. In this case, because the constants are different (3 versus 1), we can conclude that the expressions are not equivalent.

This method involves simplifying and comparing expressions, a core aspect of algebraic manipulation.