Question

Write an expression equivalent to 3/5(3y + 15).

a) 9/5y + 9
b) 9/5y + 15
c) 3/5y + 9
d) 3/5y + 15

Answer 1

The equivalent expression to
`\( (3)/(5)(3y + 15) \)` is
`\( (3)/(5)y + 15 \).` The correct option is B.

Step-by-step explanation:

To find the equivalent expression, distribute the
`\( (3)/(5) \)` to both terms inside the parentheses:

`\[ (3)/(5)(3y + 15) = (3)/(5) \cdot 3y + (3)/(5) \cdot 15 \]`

Simplify each term:

`\[ (9)/(5)y + 9 \]`

Therefore, the correct equivalent expression is
`\( (9)/(5)y + 9 \)`, and the corresponding option is (b).

The given expression
`\( (3)/(5)(3y + 15) \)`involves distributing
`\( (3)/(5) \)` to both terms inside the parentheses. This is a common algebraic operation where each term inside the parentheses is multiplied by the factor outside. Applying this, we get
`\( (3)/(5) \cdot 3y + (3)/(5) \cdot 15 \).` Simplifying each term, we obtain
`\( (9)/(5)y + 9 \).`

The final answer is
`\( (9)/(5)y + 9 \)`, corresponding to option (b) in the provided choices. It's essential to recognize the distribution property in algebra, as it allows us to simplify expressions and manipulate equations effectively.

In summary, by distributing
`\( (3)/(5) \)` to each term within the parentheses and simplifying, we arrive at the equivalent expression
`\( (9)/(5)y + 9 \)`, confirming the correct answer as option (b).