Two equivalent expressions are shown in the equation where a and b are both integers.

a(7x + 3) = b + 14x

What are the values of a and b?

The value of a is _____

The value of b is _____

7 x a + 3 a = b +14 x

well 7 x a = 14 x
so a = 2
then if a = 2
3 * 2 = b
b = 6

there is one equation and three unknowns

the number of unique equations must equal the number of unknowns
... in order to solve for all the unknowns

To find the values of a and b, we can compare the coefficients of x on both sides of the equation.

On the left side of the equation, we have a(7x + 3). The coefficient of x is 7a.

On the right side of the equation, we have b + 14x. The coefficient of x is 14.

Since the two expressions are equivalent, the coefficients of x on both sides of the equation must be equal.

Therefore, we can set up the equation:

7a = 14

Dividing both sides of the equation by 7, we get:

a = 2

Now, we can substitute this value of a back into the original equation to solve for b:

2(7x + 3) = b + 14x

Expanding the expression on the left side, we get:

14x + 6 = b + 14x

Subtracting 14x from both sides of the equation, we get:

6 = b

Therefore, the values of a and b are:

The value of a is 2.
The value of b is 6.

To find the values of a and b in the equation a(7x + 3) = b + 14x, we need to apply some algebraic steps.

First, we can distribute a to get 7ax + 3a = b + 14x.

Next, let's rearrange the equation by collecting like terms: 7ax - 14x = b - 3a.

Now, we can factor out x on the left side: x(7a - 14) = b - 3a.

To solve for a and b, we need one more equation. Do you have any additional information or equations that could help?