What value of a would make the expression a(x+3) equivalent to 7x+21 ?
(Written response)
To find the value of a that would make the expressions equivalent, we need to set them equal to each other.
a(x+3) = 7x+21
To distribute the a on the left side of the equation, we get:
ax + 3a = 7x + 21
Next, we can subtract ax from both sides of the equation and subtract 21 from both sides:
3a = 7x - ax + 21
Combining like terms, we have:
3a = (7 - a)x + 21
Since we want the expressions to be equivalent for all x values, the coefficients of x on both sides of the equation should be the same. Therefore, 7 - a = 0.
Solving for a, we have:
7 - a = 0
a = 7
So, the value of a that makes the expression a(x+3) equivalent to 7x+21 is a = 7.