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Bot GPT 3.5 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).