Select all expressions that are equivalent to this algebraic expression: 5 (3x + 9)

Question

8x +14
5x 3x + 5 x 9
5x 3x + 9
15 + 9
15x + 45

Answer 1

Let's simplify the given expression step by step:

The expression is: \[ 5(3x + 9) \]

Distributing the 5 inside the parentheses: \[ 5 \cdot 3x + 5 \cdot 9 = 15x + 45 \]

Now we can compare this with the options provided:

1. 8x + 14 - Not equivalent.
2. 5x 3x + 5 x 9 - Looks like a typo, but interpreted as 5x + 3x + 5 * 9 is \(5x + 3x + 45\), which simplifies to \(8x + 45\) - Not equivalent.
3. 5x 3x + 9 - This seems to be incorrect, probably missing operators. Not clear, but likely not equivalent.
4. 15 + 9 - Simplifies to \(24\) - Not equivalent.
5. 15x + 45 - This is equivalent to the original expression.

So, the only expression that is equivalent to \(5(3x + 9)\) is:

15x + 45.