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

Answer 1

To make the expression equivalent, we need to distribute the "a" term to the terms inside the parentheses:

a(x + 3) = ax + 3a.

Since we want this expression to be equal to 7x + 21, we set it equal to the given expression and solve for "a":

ax + 3a = 7x + 21.

To isolate the "a" term, we need to subtract ax from both sides:

3a = 7x + 21 - ax.

Now, we can factor "a" out of the right side:

3a = x(7 - a) + 21.

To have an equivalent expression, the coefficient of "a" should be 1. Therefore, we need to divide both sides by 3:

3a/3 = [x(7 - a) + 21]/3.

Simplifying, we have:

a = [x(7 - a) + 21]/3.

To further simplify, multiply both sides by 3:

3a = x(7 - a) + 21.

Expand the right side:

3a = 7x - ax + 21.

Rearrange the terms with respect to "a":

3a + ax = 7x + 21.

Factor out "a" from the left side:

a(3 + x) = 7x + 21.

Now, divide both sides by (3 + x):

a = (7x + 21)/(3 + x).

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