What value of a would make the expression a(x+3) equivalent to 7x+21?(1 point)
a(x+3) = 7x+21
ax + 3a = 7x + 21
for this to be an identity: match the variable terms and the constant terms
3a = 21 ---> a = 7
ax = 7x ---> a = 7
a = 7
We can start by distributing the "a" to the expression inside the parentheses:
a(x+3) = ax + 3a
Now we can set this expression equal to 7x + 21 and solve for a:
ax + 3a = 7x + 21
We can simplify by subtracting ax from both sides:
3a = 7x - ax + 21
And then by factoring out the "a" on the right side:
3a = (7 - x)a + 21
Now we can divide both sides by (7-x) to isolate "a":
a = 21/(7-x)
So the value of "a" that would make the expression a(x+3) equivalent to 7x+21 is a = 21/(7-x), as long as x is not equal to 7.