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

Answer 1

To determine the value of a, we need to simplify the expression a(x+3) and compare it to 7x+21.

Expanding a(x+3), we get ax + 3a.
Setting this equal to 7x + 21, we have ax + 3a = 7x + 21.

To find the value of a, we need to combine like terms. To do this, we subtract ax from both sides and subtract 21 from both sides:

ax - ax + 3a = 7x - ax + 21 - 21
0 + 3a = 7x - ax

Now, we can rearrange the equation to isolate a:

3a = 7x - ax

Factoring out the common factor of x on the right side, we get:

3a = x(7 - a)

Finally, to isolate a, we divide both sides by (7 - a):

3a/(7 - a) = x

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