Question

What value of a
would make the expression a(x+3)
equivalent to 7x+21
?(1 point)

Answer 1

To find the value of a that would make the expression a(x+3) equivalent to 7x+21, we can distribute a to the terms inside the parentheses:

a(x+3) = ax + 3a

Since this expression is equivalent to 7x+21, we can set the corresponding terms equal to each other:

ax + 3a = 7x + 21

Now, we need to solve for the value of a. We can start by subtracting ax and 21 from both sides of the equation:

3a - 21 = 7x - ax

To combine like terms, we can rewrite the equation:

3a - 21 = (7 - a)x

Now, we can solve for x. Since the equation states that this expression is equivalent for all values of x, we can choose any value to solve for. For simplicity, let's choose x = 0:

3a - 21 = (7 - a)(0)

Simplifying the right side of the equation:

3a - 21 = 0

Adding 21 to both sides:

3a = 21

Dividing both sides by 3:

a = 7

Therefore, the value of a that would make the expression a(x+3) equivalent to 7x+21 is a = 7.