To make the expression a(x+3) equivalent to 7x+21, we need to find the value of a that will give us the same result when the expression is simplified.
Let's distribute a through the expression x+3:
a(x+3) = ax + 3a
Now, we can equate this expression to 7x+21 and solve for a:
ax + 3a = 7x + 21
To solve for a, we can collect the x terms on one side and the constant terms on the other side:
ax - 7x = 21 - 3a
Factor out x on the left side:
x(a - 7) = 21 - 3a
Now, if the left side and right side are equal, the coefficients of x and the constant terms must be equal:
a - 7 = 0 (1)
-3a + 21 = 0 (2)
From equation (1), we can solve for a:
a = 7
Substituting this value of a in equation (2) to confirm:
-3(7) + 21 = 0
-21 + 21 = 0
0 = 0
The equation is true, which confirms that a = 7 makes the expression a(x+3) equivalent to 7x+21.
What value of a
would make the expression a(x+3)
equivalent to 7x+21
?
1 answer