Question

If f(×)=16×-30 and g(×)=14×-6, for which value of x does (f-g)(x)=0

Answer 1

Answer:
`x=12`

Explanation:

`f(x)=16x-30\\g(x)=14x-6` are the equations that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that
`x=12`.

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

`16x-30`

Step 2: Substitute x for the numerical value we found.

`16(12)-30`

Step 3: We will multiply
`16*20` first, giving us 192.

`192-30`

Step 4: Subtract 192 from 30. Which gives us 162.

`162`

The right side of the equal sign:

Step 1: Write the equation down:

`14x-6`

Step 2: Substitute x for the numerical value we found.

`14(12)-6`

Step 3: We will multiply
`14*12` first, giving us 168.

`168-6`

Step 4: Subtract 168 from 6. Which gives us 162.

`162`

We know that
`x=12` because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.

`162=162`