Certainly! Let's break down the solution step-by-step to evaluate the given expression:
[tex]\[
\frac{22 - (-14)}{6x - 2} - \frac{4^2 \times (-12)}{72 \div (-8) \times 3}
\][/tex]
### Step 1: Simplify the first fraction
First, consider the numerator and denominator separately:
- The numerator is [tex]\( 22 - (-14) \)[/tex]. Subtraction of a negative number changes to addition, so it becomes:
[tex]\[
22 - (-14) = 22 + 14 = 36
\][/tex]
- The denominator is [tex]\( 6x - 2 \)[/tex]. We must ensure [tex]\( 6x - 2 \neq 0 \)[/tex] to avoid division by zero. For example, if [tex]\( x = 1 \)[/tex]:
[tex]\[
6(1) - 2 = 6 - 2 = 4
\][/tex]
Thus, the first fraction is:
[tex]\[
\frac{36}{4} = 9
\][/tex]
### Step 2: Simplify the second fraction
Now, simplify the second fraction step-by-step:
- The numerator is [tex]\( 4^2 \times (-12) \)[/tex]:
[tex]\[
4^2 = 16 \quad \text{so} \quad 16 \times (-12) = -192
\][/tex]
- For the denominator, compute the operations within it:
[tex]\[
72 \div (-8) \times 3
\][/tex]
First, perform the division:
[tex]\[
72 \div (-8) = -9
\][/tex]
Then, multiply by 3:
[tex]\[
-9 \times 3 = -27
\][/tex]
Thus, the second fraction is:
[tex]\[
\frac{-192}{-27}
\][/tex]
- Simplify the fraction:
[tex]\[
\frac{-192}{-27} = 7.111111111111111
\][/tex]
### Step 3: Combine the results
Now, we subtract the evaluated second fraction from the evaluated first fraction:
[tex]\[
9 - 7.111111111111111 = 1.8888888888888893
\][/tex]
### Step 4: Summary of results
- First fraction: [tex]\( \frac{36}{4} = 9 \)[/tex]
- Second fraction: [tex]\( \frac{-192}{-27} = 7.111111111111111 \)[/tex]
- Final Result: [tex]\( 9 - 7.111111111111111 = 1.8888888888888893 \)[/tex]
Therefore, the evaluation of the given expression is:
[tex]\[
\boxed{1.8888888888888893}
\][/tex]
