What value of a would make he expression a (x + 3) equivalent to 7x + 21
To find the value of a that would make the expression a(x + 3) equivalent to 7x + 21, we need to distribute the a to both terms inside the parentheses:
a(x + 3) = ax + 3a
Since this expression is equivalent to 7x + 21, we can set up an equation:
ax + 3a = 7x + 21
Now, let's solve for a. First, we can subtract 7x from both sides to isolate the terms with the variable a:
ax - 7x + 3a = 21
Next, we need to group the terms with a together:
(ax + 3a) - 7x = 21
Now, we factor out the common factor of a:
a(x + 3) - 7x = 21
Since we know that a(x + 3) is equivalent to 7x + 21, we can substitute 7x + 21 for a(x + 3):
(7x + 21) - 7x = 21
Simplifying further:
21 = 21
This equation is true, which means that any value of a would make the expression a(x + 3) equivalent to 7x + 21.
that answer is incorrect
Apologies for the mistake. Let's correct it.
We have the expression a(x + 3) and want it to be equivalent to 7x + 21. To find the value of a, we need to distribute a to both terms inside the parentheses:
a(x + 3) = ax + 3a
We set this expression equal to 7x + 21 and solve for a:
ax + 3a = 7x + 21
To simplify further, we can combine like terms:
ax - 7x + 3a = 21
Now, we can isolate the terms involving a:
3a = 21 - ax + 7x
Next, let's factor out 'a' from the terms on the right side:
3a = 21 + x(7 - a)
To make the expression equivalent, we need the coefficient of 'a' on the right side to be equal to 3. Therefore, we set up an equation:
7 - a = 3
We solve for 'a' by subtracting 7 from both sides:
-a = -4
Multiplying both sides by -1, we get:
a = 4
Therefore, the value of a that would make the expression a(x + 3) equivalent to 7x + 21 is a = 4.
still incorrect
Apologies for the mistake once again. Let's correct it.
We have the expression a(x + 3) and want it to be equivalent to 7x + 21. To find the value of a, we need to distribute a to both terms inside the parentheses:
a(x + 3) = ax + 3a
We set this expression equal to 7x + 21 and solve for a:
ax + 3a = 7x + 21
To simplify further, we can combine like terms:
ax + 3a - 7x = 21
Now, let's isolate the terms involving 'a':
ax + 3a - 7x = 21
-7x + ax + 3a = 21
To make the terms involving 'a' match, the coefficients of 'x' must also match. Therefore, we can set up an equation:
a = 7
Substituting 'a' with 7 in the equation:
-7x + 7x + 21 = 21
The terms involving 'x' cancel out, and we're left with:
21 = 21
This equation is true, which means any value of 'a' would make the expression a(x + 3) equivalent to 7x + 21.