Question

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

Answer 1

Answer: $x=12$

Step-by-step 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.

$162=162$