Question

What value completes this equation?

Answer 1

a = 9

Explanation:

Properties of equality can be used to solve an equation.

Isolating the Variable

In order to solve the equation, we need to isolate the variable. In this equation, there are 2 variables, x and a, but we are solving for a. To isolate the variable, we can use the properties of equality, also called the PoEs. The PoEs state that we can manipulate an equation in any way so long as the same thing is done to both sides. For example, we can divide by 6, so long as we divide both sides of the equation by 6.

Solving For a

First to solve for a, we should distribute the
`(3)/(4)`. This means multiplying the 12x and 20 by 3/4.

• 9x - 15 = ax - 15

To completely isolate the variable, we can now add 15 to both sides.

• 9x = ax

Finally, divide by x.

• 9 = a

From this, we can see that a = 9 makes this equation true.