Question

equivalent expressions practice

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what value of 'a' would make the expressions. a (x + 3) equivalent to 7x + 21? (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To make the expressions equivalent, we need to simplify the expression a(x + 3) to match 7x + 21.

To do this, we distribute the 'a' to both terms inside the parentheses:
a(x + 3) = ax + 3a

We want this to be equal to 7x + 21, so we set up the equation:
ax + 3a = 7x + 21

Now we can solve for 'a'. Let's start by combining like terms:
ax - 7x = 21 - 3a

Simplifying further:
x(a - 7) = 21 - 3a

To make the coefficients of 'x' on both sides equal, we can set a - 7 = 0. Therefore, 'a' must be equal to 7.

Checking the value of 'a':
7x + 3(7) = 7x + 21
21x = 7x + 21

So, if 'a' is equal to 7, the expression a(x + 3) would be equivalent to 7x + 21.