Question
Select all expressions that are equivalent to this algebraic expression: 5(3x+9) (1 point) Responses 8x+14 8 x plus 14 5×3x+5×9 5 times 3 x plus 5 times 9 5×3x+9 5 times 3 x plus 9 15x+9 15 x plus 9 15x+45
Answers
GPT-4o mini
To determine which expressions are equivalent to the algebraic expression \( 5(3x+9) \), we can simplify the original expression first:
1. Distribute the \( 5 \):
\[
5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45
\]
Now, let's evaluate the responses provided:
1. **8x + 14** - Not equivalent.
2. **5×3x + 5×9** - This simplifies to \( 15x + 45 \), which is equivalent.
3. **5×3x + 9** - This simplifies to \( 15x + 9 \), not equivalent.
4. **15x + 9** - Not equivalent.
5. **15x + 45** - This is equivalent.
The equivalent expressions are:
- **5×3x + 5×9**
- **15x + 45**
1. Distribute the \( 5 \):
\[
5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45
\]
Now, let's evaluate the responses provided:
1. **8x + 14** - Not equivalent.
2. **5×3x + 5×9** - This simplifies to \( 15x + 45 \), which is equivalent.
3. **5×3x + 9** - This simplifies to \( 15x + 9 \), not equivalent.
4. **15x + 9** - Not equivalent.
5. **15x + 45** - This is equivalent.
The equivalent expressions are:
- **5×3x + 5×9**
- **15x + 45**