Question

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

Answer 1

To make the expression a(x+3) equivalent to 7x+21, we need to find the value of a that will give us the same result when the expression is simplified.

Let's distribute a through the expression x+3:

a(x+3) = ax + 3a

Now, we can equate this expression to 7x+21 and solve for a:

ax + 3a = 7x + 21

To solve for a, we can collect the x terms on one side and the constant terms on the other side:

ax - 7x = 21 - 3a

Factor out x on the left side:

x(a - 7) = 21 - 3a

Now, if the left side and right side are equal, the coefficients of x and the constant terms must be equal:

a - 7 = 0 (1)

-3a + 21 = 0 (2)

From equation (1), we can solve for a:

a = 7

Substituting this value of a in equation (2) to confirm:

-3(7) + 21 = 0

-21 + 21 = 0

0 = 0

The equation is true, which confirms that a = 7 makes the expression a(x+3) equivalent to 7x+21.